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   Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance; Thalmaier, Anton  ; in Journal of Functional Analysis (2023), 285(5), 109997 For a complete connected Riemannian manifold M let V∊ C^2(M) be such that µ(dx)=exp(-V(x))vol(dx) is a probability measure on M. Taking µ as reference measure, we derive inequalities for probability ... [more ▼] For a complete connected Riemannian manifold M let V∊ C^2(M) be such that µ(dx)=exp(-V(x))vol(dx) is a probability measure on M. Taking µ as reference measure, we derive inequalities for probability measures on M linking relative entropy, Fisher information, Stein discrepancy and Wasserstein distance. These inequalities strengthen in particular the famous log-Sobolev and transportation-cost inequality and extend the so-called Entropy/Stein-discrepancy/Information (HSI) inequality established by Ledoux, Nourdin and Peccati (2015) for the standard Gaussian measure on Euclidean space to the setting of Riemannian manifolds. [less ▲] Detailed reference viewed: 122 (27 UL)Transport inequalities for random point measures; ; Peccati, Giovanni in Journal of Functional Analysis (2021), 281(9), Detailed reference viewed: 41 (1 UL)Spectral gap on Riemannian path space over static and evolving manifoldsCheng, Li Juan ; Thalmaier, Anton in Journal of Functional Analysis (2018), 274(4), 959-984 In this article, we continue the discussion of Fang–Wu (2015) to estimate the spectral gap of the Ornstein–Uhlenbeck operator on path space over a Riemannian manifold of pinched Ricci curvature. Along ... [more ▼] In this article, we continue the discussion of Fang–Wu (2015) to estimate the spectral gap of the Ornstein–Uhlenbeck operator on path space over a Riemannian manifold of pinched Ricci curvature. Along with explicit estimates we study the short-time asymptotics of the spectral gap. The results are then extended to the path space of Riemannian manifolds evolving under a geometric flow. Our paper is strongly motivated by Naber’s recent work (2015) on characterizing bounded Ricci curvature through stochastic analysis on path space. [less ▲] Detailed reference viewed: 344 (43 UL)Squared chaotic random variables: new moment inequalities with applications; Nourdin, Ivan ; Peccati, Giovanni et alin Journal of Functional Analysis (2016), 270(2), 649-670 Detailed reference viewed: 232 (18 UL)Stein-Malliavin Approximations for Nonlinear Functionals of Random Eigenfunctions on S^d; Rossi, Maurizia in Journal of Functional Analysis (2015) Detailed reference viewed: 71 (7 UL) Fourth Moment Theorems for Markov diffusion generatorsAzmoodeh, Ehsan ; Campese, Simon ; Poly, Guillaume Joseph in Journal of Functional Analysis (2014), 266(4), 23412359 Inspired by the insightful article [4], we revisit the Nualart–Peccati criterion [13] (now known as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov diffusion ... [more ▼] Inspired by the insightful article [4], we revisit the Nualart–Peccati criterion [13] (now known as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov diffusion generators. We are not only able to drastically simplify all of its previous proofs, but also to provide new settings of diffusive generators (Laguerre, Jacobi) where such a criterion holds. Convergence towards Gamma and Beta distributions under moment conditions is also discussed. [less ▲] Detailed reference viewed: 187 (27 UL)Entropy and the fourth moment phenomenonNourdin, Ivan ; Peccati, Giovanni ; Swan, Yvik in Journal of Functional Analysis (2014), 266(5), 3170-3207 Detailed reference viewed: 213 (11 UL)Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle; Peccati, Giovanni in Journal of Functional Analysis (2014), 267(4), Detailed reference viewed: 123 (0 UL)Properties of convergence in Dirichlet structures; Poly, Guillaume Joseph in Journal of Functional Analysis (2013) Detailed reference viewed: 109 (0 UL)Coupling of Brownian motions and Perelman's L-functional; Philipowski, Robert in Journal of Functional Analysis (2011), 260 We show that on a manifold whose Riemannian metric evolves under backwards Ricci flow two Brownian motions can be coupled in such a way that their normalized L-distance is a supermartingale. As a ... [more ▼] We show that on a manifold whose Riemannian metric evolves under backwards Ricci flow two Brownian motions can be coupled in such a way that their normalized L-distance is a supermartingale. As a corollary, we obtain the monotonicity of the transportation cost between two solutions of the heat equation in the case that the cost function is the composition of a concave non-decreasing function and the normalized L-distance. In particular, it provides a new proof of a recent result of Topping [P. Topping, L-optimal transportation for Ricci flow, J. Reine Angew. Math. 636 (2009) 93–122]. [less ▲] Detailed reference viewed: 79 (14 UL)Stochastic differential equations with coefficients in Sobolev spaces; ; Thalmaier, Anton in Journal of Functional Analysis (2010), 259(5), 1129-1168 Detailed reference viewed: 284 (5 UL)Cumulants on the Wiener spaceNourdin, Ivan ; Peccati, Giovanni in Journal of Functional Analysis (2010), 258(11), 3775--3791 Detailed reference viewed: 163 (1 UL)Brownian measures on Jordan-Virasoro curves associated to the Weil-Petersson metric; ; Thalmaier, Anton in Journal of Functional Analysis (2010), 259(12), 3037-3079 Detailed reference viewed: 251 (9 UL)Representations of quantum permutation algebrasSchlenker, Jean-Marc ; ; in Journal of Functional Analysis (2009), 257(9), 2864-2910 We develop a combinatorial approach to the quantum permutation algebras, as Hopf images of representations of type π:As(n)→B(H)π:As(n)→B(H). We discuss several general problems, including the ... [more ▼] We develop a combinatorial approach to the quantum permutation algebras, as Hopf images of representations of type π:As(n)→B(H)π:As(n)→B(H). We discuss several general problems, including the commutativity and cocommutativity ones, the existence of tensor product or free wreath product decompositions, and the Tannakian aspects of the construction. The main motivation comes from the quantum invariants of the complex Hadamard matrices: we show here that, under suitable regularity assumptions, the computations can be performed up to n=6. [less ▲] Detailed reference viewed: 101 (1 UL)A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to 1/4Nourdin, Ivan in Journal of Functional Analysis (2009), 256 Detailed reference viewed: 109 (2 UL)Second order Poincaré inequalities and CLTs on Wiener spaceNourdin, Ivan ; Peccati, Giovanni ; in Journal of Functional Analysis (2009), 257(2), 593--609 Detailed reference viewed: 179 (2 UL)Itô's and Tanaka's type formulae for the stochastic heat equation: the linear case; Nourdin, Ivan ; in Journal of Functional Analysis (2005), 228(1), 114-143 Detailed reference viewed: 95 (1 UL)Heat equation derivative formulas for vector bundles; Thalmaier, Anton in Journal of Functional Analysis (2001), 183(1), 42-108 Detailed reference viewed: 342 (31 UL)Gradient estimates for harmonic functions on regular domains in Riemannian manifoldsThalmaier, Anton ; in Journal of Functional Analysis (1998), 155(1), 109-124 Detailed reference viewed: 290 (15 UL) |
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