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Publications
In press
Dimension-free Harnack inequalities for conjugate heat equations and their applications to geometric flows;
in Analysis and PDE (in press)
Limit theorems for additive functionals of the fractional Brownian motion; ; ;
in Annals of Probability (in press)
Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance;
in Annals of Applied Probability (in press)
Phase transitions and noise sensitivity on the Poisson space via stopping sets and decision trees; ;
in Random Structures and Algorithms (in press)
2023
Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds; ;
in Stochastic Partial Differential Equations: Analysis and Computations (2023), 11(2), 685-713
Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance; ;
in Journal of Functional Analysis (2023), 285(5), 109997
Small Scale CLTs for the Nodal Length of Monochromatic Waves; ; ;
in Communications in Mathematical Physics (2023), 397(1), 1-36
The discrepancy between min-max statistics of Gaussian and Gaussian-subordinated matrices;
in Stochastic Processes and Their Applications (2023), 158
2022
Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling; ; ;
E-print/Working paper (2022)
Hessian estimates for Dirichlet and Neumann eigenfunctions of Laplacian;
E-print/Working paper (2022)
Second Order Bismut formulae and applications to Neumann semigroups on manifolds; ;
E-print/Working paper (2022)
Functional Convergence of U-processes with Size-Dependent Kernels; ;
in Annals of Applied Probability (2022), 32(1), 551-601
The multivariate functional de Jong CLT; ;
in Probability Theory and Related Fields (2022), 184(1), 367-399
Quantitative two-scale stabilization on the Poisson space; ;
in Annals of Applied Probability (2022)
Multivariate normal approximation on the Wiener space: new bounds in the convex distance; ;
in Journal of Theoretical Probability (2022)
2021
Malliavin-Stein method: a survey of some recent developments; ;
in Modern Stochastics: Theory and Applications (2021), 8(2), 141-177
Brownian Loops, Layering Fields and Imaginary Gaussian Multiplicative Chaos; ; ;
in Communications in Mathematical Physics (2021), 381(3), 889-945
Hessian heat kernel estimates and Calderón-Zygmund inequalities on complete Riemannian manifolds; ;
E-print/Working paper (2021)
Functional inequalities on path space of sub-Riemannian manifolds and applications; ;
in Nonlinear Analysis: Theory, Methods and Applications (2021), 210(112387), 1-30
Exponential contraction in Wasserstein distance on static and evolving manifolds; ;
in Revue Roumaine de Mathématiques Pures et Appliquées (2021), 66(1), 107-129
Transport inequalities for random point measures; ;
in Journal of Functional Analysis (2021), 281(9),
Approximation of Fractional Local Times: Zero Energy and Derivatives; ;
in Annals of Applied Probability (2021), In press
The Breuer-Major Theorem in total variation: improved rates under minimal regularity; ;
in Stochastic Processes and Their Applications (2021), 131
2020
Gradient Estimates on Dirichlet and Neumann Eigenfunctions; ;
in International Mathematics Research Notices (2020), 2020(20), 7279-7305
Radial processes for sub-Riemannian Brownian motions and applications; ; ; ;
in Electronic Journal of Probability (2020), 25(paper no. 97), 1-17
Scattering theory without injectivity radius assumptions, and spectral stability for the Ricci flow;
in Annales de l'Institut Fourier (2020), 70(1), 437-456
Restricted hypercontractivity on the Poisson space; ;
in Proceedings of the American Mathematical Society (2020), 148
Gaussian Random Measures Generated by Berry's Nodal Sets;
in Journal of Statistical Physics (2020), 178(4), 996-1027
Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces;
in Bernoulli (2020), 26(3), 2202-2225
2019
Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations; ; ;
in Calculus of Variations and Partial Differential Equations (2019), 58:130(4), 1-38
Phase singularities in complex arithmetic random waves; ; ;
in Electronic Journal of Probability (2019), 24(71), 1-45
Quantitative CLTs for symmetric U-statistics using contractions;
in Electronic Journal of Probability (2019), 24
Quantitative limit theorems for symmetric U-statistics using contractions;
in Electronic Journal of Probability (2019), 24
Stochastic completeness and gradient representations for sub-Riemannian manifolds;
in Potential Analysis (2019), 51(2), 219-254
Nodal Statistics of Planar Random Waves; ;
in Communications in Mathematical Physics (2019), 369(1), 99-151
Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality; ;
in Electronic Communications in Probability (2019), 24(34), 1-12
Derivative and divergence formulae for diffusion semigroups;
in Annals of Probability (2019), 47(2), 743-773
2018
Characterization of pinched Ricci curvature by functional inequalities;
in Journal of Geometric Analysis (2018), 28(3), 2312-2345
Evolution systems of measures and semigroup properties on evolving manifolds;
in Electronic Journal of Probability (2018), 23(20), 1-27
Spectral gap on Riemannian path space over static and evolving manifolds;
in Journal of Functional Analysis (2018), 274(4), 959-984
Functional inequalities on manifolds with non-convex boundary; ;
in Science China Mathematics (2018), 61(8), 1421-1436
Quantitative C1-estimates by Bismut formulae; ;
in Journal of Mathematical Analysis and Applications (2018), 465(2), 803-813
Uniform gradient estimates on manifolds with a boundary and applications; ;
in Analysis and Mathematical Physics (2018), 8(4), 571-588
Fourth moment theorems on the Poisson space: analytic statements via product formulae;
in Electronic Communications in Probability (2018), 23
Concentration of the Intrinsic Volumes of a Convex Body; ; ; ;
in Geometric Aspects of Functional Analysis – Israel Seminar (GAFA) 2017-2019 (2018)
Quantitative limit theorems for local functionals of arithmetic random waves;
in Celledoni, Elena (Ed.) Computation and combinatorics in dynamics, stochastics and control. (2018)
2017
Gaussian Phase Transitions and Conic Intrinsic Volumes: Steining the Steiner Formula; ;
in Annals of Applied Probability (2017), 27(1), 1-47
New Kolmogorov bounds for functionals of binomial point processes;
in Annals of Applied Probability (2017), 27(4), 1992-20131
2016
The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds; ;
in ALEA: Latin American Journal of Probability and Mathematical Statistics (2016), 13
Gaussian approximations of nonlinear statistis on the sphere; ; ;
in Journal of Mathematical Analysis and Applications (2016), 436(2), 1121-1148
Multivariate Gaussian approxi- mations on Markov chaoses; ; ;
in Electronic Communications in Probability (2016), 21
Submersions, Hamiltonian systems and optimal solutions to the rolling manifolds problemin SIAM Journal on Control and Optimization (2016), 54(2), 536-566
Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part I;
in Mathematische Zeitschrift (2016), 282(1), 99-130
Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part II;
in Mathematische Zeitschrift (2016), 282(1), 131-164
Discrete versions of the transport equation and the Shepp-Olkin conjecture;
in Annals of Probability (2016), 44(1), 276-306
Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization; ;
in Probability Theory and Related Fields (2016), 165(3), 667-723
Squared chaotic random variables: new moment inequalities with applications; ; ;
in Journal of Functional Analysis (2016), 270(2), 649-670
Non-universality of nodal length distribution for arithmetic random waves; ; ;
in Geometric and Functional Analysis (2016), 26(3), 926-960
Quantitative stable limit theorems on the Wiener space; ;
in Annals of Probability (2016), 44(1), 1-41
Strong asymptotic independence on Wiener chaos; ;
in Proceedings of the American Mathematical Society (2016), 144(2), 875-886
Classical and free fourth moment theorems: universality and thresholds; ; ;
in Journal of Theoretical Probability (2016), 29(2), 653-680
Multidimensional limit theorems for homogeneous sums : a general transfer principle; ; ;
in ESAIM: Probability and Statistics (2016), 20
Concentration bounds for geometric Poisson functionals: logarithmic Sobolev inequalities revisited;
in Electronic Journal of Probability (2016), 6(44),
Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry;
Book published by Springer (2016)
Geometry of subelliptic diffusionsin Barilari, Davide; Boscain, Ugo; Sigalotti, Mario (Eds.) Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Volume II (2016)
2015
Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach.; ;
in Séminaire de Probabilités (2015)
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model; ;
in Modern Stochastics: Theory and Applications (2015), 2(1), 2949
Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind;
in Statistical Inference for Stochastic Processes (2015), 18(3), 205227
Sub-Riemannian Geometry on Infinite-Dimensional Manifolds; ;
in Journal of Geometric Analysis (2015), 25(4), 2474-2515
An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions; ;
in Potential Analysis (2015), 42(2), 483-497
Martingales on manifolds with time-dependent connection; ;
in Journal of Theoretical Probability (2015), 28(3), 1038-1062
On gradient solitons of the Ricci-Harmonic flow; ;
in Acta Mathematica Sinica (2015), 31(11), 1798-1804
Stein's method, logarithmic Sobolev and transport inequalities; ;
in Geometric and Functional Analysis (2015), 25
The optimal fourth moment theorem;
in Proceedings of the American Mathematical Society (2015), 143(7), 3123-3133
Heat equation in vector bundles with time-dependent metric;
in Journal of the Mathematical Society of Japan (2015), 67(4), 1759-1769
2014
Equivalent Harnack and gradient inequalities for pointwise curvature lower bound; ;
in Bulletin des Sciences Mathématiques (2014), 138(5), 643-655
Fourth Moment Theorems for Markov diffusion generators; ;
in Journal of Functional Analysis (2014), 266(4), 23412359
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model; ;
E-print/Working paper (2014)
Necessary and sufficient conditions for Hölder continuity of Gaussian processes; ; ;
in Statistics and Probability Letters (2014), 94
Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering;
in Electronic Journal of Probability (2014), 19(Paper 66),
Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle;
in Journal of Functional Analysis (2014), 267(4),
Normal approximations for wavelet coefficients on spherical Poisson fields; ;
in Journal of Mathematical Analysis and Applications (2014), 409(1), 212--227
Exchangeable Hoeffding decompositions over finite sets: a characterization and counterexamples; ;
in Journal of Multivariate Analysis (2014), 131
Geometric conditions for the existence of a rolling without twisting or slipping;
in Communications on Pure and Applied Analysis (2014), 13(1), 435-452
Harnack estimates for geometric flows, applications to Ricci flow coupled with harmonic map flow;
in Geometriae Dedicata (2014), 169(1), 411-418
A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric; ;
in Stochastic Processes and Their Applications (2014), 124(11), 3535-3552
Ito's formula for Walsh's Brownian motion and applications;
in Statistics and Probability Letters (2014)
A natural derivative on [0, n] and a binomial Poincaré inequality; ;
in ESAIM: Probability and Statistics (2014), 18
Entropy and the fourth moment phenomenon; ;
in Journal of Functional Analysis (2014), 266(5), 3170-3207
Integration by parts and representation of information functionals; ;
in Abstract book of 2014 IEEE International Symposium on Information Theory (ISIT) (2014)
Comparison inequalities on the Wiener space; ;
in Stochastic Processes and Their Applications (2014), 124(4), 1566-1581
Quantitative CLTs on a Gaussian space: a survey of recent developmentsin ESAIM: Proceedings and Surveys (2014), 44
2013
On the fractional Black-Scholes market with transaction costsin Communications in Mathematical Finance (2013), 2(3), 21-40
Drift parameter estimation for fractional Ornstein–Uhlenbeck process of the second kind;
in Statistics: A Journal of Theoretical and Applied Statistics (2013)
Spectral characterization of the quadratic variation of mixed Brownian–fractional Brownian motion;
in Statistical Inference for Stochastic Processes (2013), 16(2), 97-112
Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind;
E-print/Working paper (2013)
Rate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion;
in Journal of Theoretical Probability (2013)
Entropy and lowest eigenvalue on evolving manifolds; ;
in Pacific Journal of Mathematics (2013), 264(1), 61-81
A note on Chow's entropy functional for the Gauss curvature flow; ;
in Comptes Rendus de l'Académie des Sciences. Série I. Mathématique (2013), 351(21-22), 833-835
Tanaka's SDE on the circle and stochastic flows;
in Latin American Journal of Probability and Mathematical Statistics (2013)
Fine Gaussian fluctuations on the Poisson space II: Rescaled kernels, marked processes and geometric $U$-statistics;
in Stochastic Processes and Their Applications (2013), 123(12), 4186--4218
Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs;
in Electronic Journal of Probability (2013), 18
Mean-square continuity on homogeneous spaces of compact groups;
in Electronic Communications in Probability (2013), 18
Multidimensional semicircular limits on the free Wigner chaos; ;
in The Ascona Proceedings, 2011 (2013)
Gamma limits and $U$-statistics on the Poisson space;
in Latin American Journal of Probability and Mathematical Statistics (2013), 10(1), 525--560
2012
The differentiation of hypoelliptic diffusion semigroups;
in Don Burkholder: A Collection of Articles in His Honor (2012)
Optimal Berry-Esseen rates on the Wiener space: the barrier of third and fourth cumulants; ; ;
in Latin American Journal of Probability and Mathematical Statistics (2012), 9(2), 473--500
Discrete approximations to solution flows of Tanaka's SDE related to Walsh Brownian motionin Séminaire de Probabilités XLIV (2012)
Concavity of entropy along binomial convolutionin Electronic communications in probability (2012), 17
2011
Coupling of Brownian motions and Perelman's L-functional;
in Journal of Functional Analysis (2011), 260
Non-explosion of diffusion processes on manifolds with time-dependent metric;
in Mathematische Zeitschrift (2011), 268
Quantitative Breuer-Major theorems; ;
in Stochastic Processes and Their Applications (2011), 121(4), 793--812
Hoeffding spaces and Specht modules;
in ESAIM: Probability and Statistics (2011), 15(In honor of Marc Yor, suppl.), 58--68
Stochastic particle approximations for the Ricci flow on surfaces and the Yamabe flowin Potential Analysis (2011), 35
Paul Malliavin (10 September 1925 - 3 June 2010)in European Mathematical Society. Newsletter (2011), 81
A stochastic approach to a priori estimates and Liouville theorems for harmonic maps;
in Bulletin des Sciences Mathématiques (2011), 135(6-7), 816-843
2010
Brownian measures on Jordan-Virasoro curves associated to the Weil-Petersson metric; ;
in Journal of Functional Analysis (2010), 259(12), 3037-3079
The differentiation of hypoelliptic diffusion semigroups;
in Illinois Journal of Mathematics (2010), 54(4), 1285-1311
Li-Yau type gradient estimates and Harnack inequalities by stochastic analysis;
in Probabilistic approach to geometry (2010)
Stochastic differential equations with coefficients in Sobolev spaces; ;
in Journal of Functional Analysis (2010), 259(5), 1129-1168
Representations of SO(3) and angular polyspectra;
in Journal of Multivariate Analysis (2010), 101(1), 77--100
Ergodicity and Gaussianity for spherical random fields;
in Journal of Mathematical Physics (2010), 51(4), 04330123
Group representations and high-resolution central limit theorems for subordinated spherical random fields;
in Bernoulli (2010), 16(3), 798--824
Stein's method meets Malliavin calculus: a short survey with new estimates;
in Recent development in stochastic dynamics and stochastic analysis (2010)
Universal Gaussian fluctuations of non-Hermitian matrix ensembles: from weak convergence to almost sure CLTs;
in Latin American Journal of Probability and Mathematical Statistics (2010), 7
Multivariate normal approximation using Stein's method and Malliavin calculus; ;
in Annales de l'Institut Henri Poincare (B) Probability & Statistics (2010), 46(1), 45--58
Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos; ;
in Annals of Probability (2010), 38(5), 1947--1985
Stein's method and stochastic analysis of Rademacher functionals; ;
in Electronic Journal of Probability (2010), 15
Stein's method and normal approximation of Poisson functionals; ; ;
in Annals of Probability (2010), 38(2), 443--478
Multi-dimensional Gaussian fluctuations on the Poisson space;
in Electronic Journal of Probability (2010), 15
2009
Existence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature; ;
in Mathematische Zeitschrift (2009), 263(2), 369-409
Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds; ;
in Stochastic Processes and Their Applications (2009), 119(10), 3653-3670
Exact confidence intervals for the Hurst parameter of a fractional Brownian motion; ;
in Electronic Journal of Statistics (2009), 3
Differentiating $\sigma$-fields for Gaussian and shifted Gaussian processes; ;
in Stochastics: an International Journal of Probablitiy and Stochastic Processes (2009), 81(1), 79--97
Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields;
in Annals of Probability (2009), 37(6), 2231--2261
Second order Poincaré inequalities and CLTs on Wiener space; ;
in Journal of Functional Analysis (2009), 257(2), 593--609
Decompositions of stochastic processes based on irreducible group representations;
in Theory of Probability & Its Applications (2009), 54(2), 304--336
2008
Brownian motion with respect to a metric depending on time: definition, existence and applications to Ricci flow; ;
in Comptes Rendus. Mathématique (2008), 346(13-14), 773-778
High-frequency asymptotics for subordinated stationary fields on an abelian compact group;
in Stochastic Processes and Their Applications (2008), 118(4), 585--613
Weighted power variations of iterated Brownian motion;
in Electronic Journal of Probability (2008), 13
Multiple integral representation for functionals of Dirichlet processesin Bernoulli (2008), 14(1), 91--124
Linear and quadratic functionals of random hazard rates: an asymptotic analysis;
in Annals of Applied Probability (2008), 18(5), 1910--1943
Limit theorems for multiple stochastic integrals;
in Latin American Journal of Probability and Mathematical Statistics (2008), 4
Stable convergence of multiple Wiener-It\^o integrals;
in Journal of Theoretical Probability (2008), 21(3), 527--570
Burkholder's submartingales from a stochastic calculus perspective;
in Illinois Journal of Mathematics (2008), 52(3), 815--824
2007
Gradient estimates for positive harmonic functions by stochastic analysis; ;
in Stochastic Processes and Their Applications (2007), 117(2), 202-220
Stable convergence of generalized $L^2$ stochastic integrals and the principle of conditioning;
in Electronic Journal of Probability (2007), 12
Anticipating integrals and martingales on the Poisson space;
in Random Operators and Stochastic Equations (2007), 15(4), 327--352
2006
Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below; ;
in Bulletin des Sciences Mathématiques (2006), 130(3), 223-233
On quadratic functionals of the Brownian sheet and related processes; ;
in Stochastic Processes and Their Applications (2006), 116(3), 493--538
Martingale structure of Skorohod integral processes; ;
in Annals of Probability (2006), 34(3), 1217--1239
Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections;
in Approximation and probability (2006)
2005
Central limit theorems for sequences of multiple stochastic integrals;
in Annals of Probability (2005), 33(1), 177--193
Gaussian limits for vector-valued multiple stochastic integrals;
in Séminaire de Probabilités XXXVIII (2005)
2004
Canonical Brownian motion on the space of univalent functions and resolution of Beltrami equations by a continuity method along stochastic flows; ;
in Journal de Mathématiques Pures et Appliquées (2004), 83(8), 955-1018
Geometrization of Monte-Carlo numerical analysis of an elliptic operator: strong approximation; ;
in Comptes Rendus. Mathématique (2004), 338(6), 481-486
Anticipative stochastic integration based on time-space chaosin Stochastic Processes and Their Applications (2004), 112(2), 331--355
Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observationsin Annals of Probability (2004), 32(3A), 1796--1829
Weak convergence to Ocone martingales: a remarkin Electronic Communications in Probability (2004), 9
Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge;
in Asymptotic methods in stochastics (2004)
Hardy's inequality in $L^2([0,1])$ and principal values of Brownian local times;
in Asymptotic methods in stochastics (2004)
Derivative estimates of semigroups and Riesz transforms on vector bundles;
in Potential Analysis (2004), 20(2), 105-123
2003
A Bismut type formula for the Hessian of heat semigroups; ;
in Comptes Rendus. Mathématique (2003), 336(8), 661-666
Yang-Mills fields and random holonomy along Brownian bridges;
in Annals of Probability (2003), 31(2), 769-790
The price-volatility feedback rate: an implementable mathematical indicator of market stability; ; ; ;
in Math. Finance (2003), 13(1), 17-35
Numerical error for SDE: asymptotic expansion and hyperdistributions;
in Comptes Rendus. Mathématique (2003), 336(10), 851-856
Hoeffding decompositions for exchangeable sequences and chaotic representation of functionals of Dirichlet processesin Comptes Rendus. Mathématique (2003), 336(10), 845--850
2002
A probabilistic approach to the Yang-Mills heat equation; ;
in Journal de Mathématiques Pures et Appliquées (2002), 81(2), 143-166
2001
Heat equation derivative formulas for vector bundles;
in Journal of Functional Analysis (2001), 183(1), 42-108
On the convergence of multiple random integralsin Studia Scientiarum Mathematicarum Hungarica (2001), 37(3-4), 429--470
A representation result for time-space Brownian chaosin Annales de l'Institut Henri Poincare (B) Probability & Statistics (2001), 37(5), 607--625
1999
Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps; ;
in Annales de l'Institut Henri Poincare (B) Probability & Statistics (1999), 35(6), 765-791
Bismut type differentiation of semigroups.;
in Probability theory and mathematical statistics. (1999)
1998
Complete lifts of connections and stochastic Jacobi fields;
in Journal de Mathématiques Pures et Appliquées (1998), 77(3), 283-315
Stability of stochastic differential equations in manifolds;
in Séminaire de Probabilités, XXXII (1998)
Some remarks on the heat flow for functions and formsin Electronic Communications in Probability (1998), 3
Gradient estimates for harmonic functions on regular domains in Riemannian manifolds;
in Journal of Functional Analysis (1998), 155(1), 109-124
1997
On the differentiation of heat semigroups and Poisson integralsin Stochastics and Stochastics Reports (1997), 61(3-4), 297-321
1996
Brownian motion and the formation of singularities in the heat flow for harmonic mapsin Probability Theory and Related Fields (1996), 105(3), 335-367
Martingales on Riemannian manifolds and the nonlinear heat equationin Stochastic analysis and applications (1996)
1994
1989
Asymptotik Brownscher Bewegungen im Zusammenhang mit geometrischen und potentialtheoretischen Eigenschaften Riemannscher Mannigfaltigkeiten negativer KrümmungBook published by Universität Regensburg Fachbereich Mathematik (1989)
