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Concentration bounds for geometric Poisson functionals: logarithmic Sobolev inequalities revisited Peccati, Giovanni ; in Electronic Journal of Probability (in press) Detailed reference viewed: 176 (14 UL)Radial processes for sub-Riemannian Brownian motions and applications ; ; et al in Electronic Journal of Probability (2020), 25(paper no. 97), 1-17 We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô's formula is proved for the radial processes associated to Riemannian distances approximating ... [more ▼] We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô's formula is proved for the radial processes associated to Riemannian distances approximating the Riemannian one. We deduce very general stochastic completeness criteria for the sub-Riemannian Brownian motion. In the context of Sasakian foliations and H-type groups, one can push the analysis further, and taking advantage of the recently proved sub-Laplacian comparison theorems one can compare the radial processes for the sub-Riemannian distance to one-dimensional model diffusions. As a geometric application, we prove Cheng's type estimates for the Dirichlet eigenvalues of the sub-Riemannian metric balls, a result which seems to be new even in the Heisenberg group. [less ▲] Detailed reference viewed: 75 (21 UL)Quantitative CLTs for symmetric U-statistics using contractions Döbler, Christian ; Peccati, Giovanni in Electronic Journal of Probability (2019) Detailed reference viewed: 72 (3 UL)Phase singularities in complex arithmetic random waves ; Nourdin, Ivan ; Peccati, Giovanni et al in Electronic Journal of Probability (2019), 24(71), 1-45 Detailed reference viewed: 122 (4 UL)Evolution systems of measures and semigroup properties on evolving manifolds Cheng, Li Juan ; Thalmaier, Anton in Electronic Journal of Probability (2018), 23(20), 1-27 An evolving Riemannian manifold (M,g_t)_{t\in I} consists of a smooth d-dimensional manifold M, equipped with a geometric flow g_t of complete Riemannian metrics, parametrized by I=(-\infty,T). Given an ... [more ▼] An evolving Riemannian manifold (M,g_t)_{t\in I} consists of a smooth d-dimensional manifold M, equipped with a geometric flow g_t of complete Riemannian metrics, parametrized by I=(-\infty,T). Given an additional C^{1,1} family of vector fields (Z_t)_{t\in I} on M. We study the family of operators L_t=\Delta_t +Z_t where \Delta_t denotes the Laplacian with respect to the metric g_t. We first give sufficient conditions, in terms of space-time Lyapunov functions, for non-explosion of the diffusion generated by L_t, and for existence of evolution systems of probability measures associated to it. Coupling methods are used to establish uniqueness of the evolution systems under suitable curvature conditions. Adopting such a unique system of probability measures as reference measures, we characterize supercontractivity, hypercontractivity and ultraboundedness of the corresponding time-inhomogeneous semigroup. To this end, gradient estimates and a family of (super-)logarithmic Sobolev inequalities are established. [less ▲] Detailed reference viewed: 320 (65 UL)Fourth moment theorems on The Poisson space in any dimension Döbler, Christian ; Vidotto, Anna ; Zheng, Guangqu in Electronic Journal of Probability (2018) Detailed reference viewed: 179 (15 UL)Recurrence and Transience of Frogs with Drift on Z^d Döbler, Christian ; ; et al in Electronic Journal of Probability (2018) Detailed reference viewed: 89 (5 UL)Quantitative de Jong theorems in any dimension Döbler, Christian ; Peccati, Giovanni in Electronic Journal of Probability (2017), 22 Detailed reference viewed: 227 (25 UL)An iterative technique for bounding derivatives of solutions of Stein equations Döbler, Christian ; ; in Electronic Journal of Probability (2017), 22 Detailed reference viewed: 138 (13 UL)Stein's method of exchangeable pairs for the Beta distribution and generalizations Döbler, Christian in Electronic Journal of Probability (2015) Detailed reference viewed: 163 (11 UL)Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering ; Peccati, Giovanni in Electronic Journal of Probability (2014), 19(Paper 66), Detailed reference viewed: 84 (2 UL)W1,+-interpolation of probability measures on graphs Hillion, Erwan in Electronic Journal of Probability (2014), 19 We generalize an equation introduced by Benamou and Brenier and characterizing Wasserstein Wp-geodesics for p > 1, from the continuous setting of probability distributions on a Riemannian manifold to the ... [more ▼] We generalize an equation introduced by Benamou and Brenier and characterizing Wasserstein Wp-geodesics for p > 1, from the continuous setting of probability distributions on a Riemannian manifold to the discrete setting of probability distributions on a general graph. Given an initial and a nal distributions (f_0(x)), (f_1(x)), we prove the existence of a curve (f_t(x)) satisfying this Benamou-Brenier equation. We also show that such a curve can be described as a mixture of binomial distributions with respect to a coupling that is solution of a certain optimization problem. [less ▲] Detailed reference viewed: 97 (4 UL)Stochastic flows on metric graphs Hajri, Hatem ; in Electronic Journal of Probability (2014) Detailed reference viewed: 127 (22 UL)An Itô's type formula for the fractional Brownian motion in Brownian time Nourdin, Ivan ; in Electronic Journal of Probability (2014), 19(99), 1-15 Detailed reference viewed: 93 (1 UL)Absolute continuity and convergence of densities for random vectors on Wiener chaos Nourdin, Ivan ; ; Poly, Guillaume Joseph et al in Electronic Journal of Probability (2013), 18(22), 1--19 Detailed reference viewed: 119 (3 UL)Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs ; Peccati, Giovanni in Electronic Journal of Probability (2013), 18 Detailed reference viewed: 121 (1 UL)Stein's method and the multivariate CLT for traces of powers on the classical compact groups Döbler, Christian ; in Electronic Journal of Probability (2011) Detailed reference viewed: 58 (2 UL)Stochastic flows related to Walsh Brownian motion Hajri, Hatem in Electronic Journal of Probability (2011) Detailed reference viewed: 93 (1 UL)Stein's method and stochastic analysis of Rademacher functionals Nourdin, Ivan ; Peccati, Giovanni ; in Electronic Journal of Probability (2010), 15 Detailed reference viewed: 147 (2 UL)The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter H=1/6 Nourdin, Ivan ; ; in Electronic Journal of Probability (2010), 15 Detailed reference viewed: 56 (5 UL) |
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