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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: 131 (10 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: 87 (4 UL)Quantitative CLTs for symmetric U-statistics using contractions Döbler, Christian ; Peccati, Giovanni in Electronic Journal of Probability (2019) Detailed reference viewed: 40 (2 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: 268 (63 UL)Recurrence and Transience of Frogs with Drift on Z^d Döbler, Christian ; ; et al in Electronic Journal of Probability (2018) Detailed reference viewed: 70 (4 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: 147 (14 UL)An iterative technique for bounding derivatives of solutions of Stein equations Döbler, Christian ; ; in Electronic Journal of Probability (2017), 22 Detailed reference viewed: 109 (12 UL)Quantitative de Jong theorems in any dimension Döbler, Christian ; Peccati, Giovanni in Electronic Journal of Probability (2017), 22 Detailed reference viewed: 186 (20 UL)Stein's method of exchangeable pairs for the Beta distribution and generalizations Döbler, Christian in Electronic Journal of Probability (2015) Detailed reference viewed: 132 (8 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: 55 (2 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: 78 (1 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: 68 (4 UL)Stochastic flows on metric graphs Hajri, Hatem ; in Electronic Journal of Probability (2014) Detailed reference viewed: 99 (22 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: 76 (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: 77 (2 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: 50 (2 UL)Stochastic flows related to Walsh Brownian motion Hajri, Hatem in Electronic Journal of Probability (2011) Detailed reference viewed: 67 (1 UL)Multi-dimensional Gaussian fluctuations on the Poisson space Peccati, Giovanni ; in Electronic Journal of Probability (2010), 15 Detailed reference viewed: 76 (0 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: 44 (3 UL)Stein's method and stochastic analysis of Rademacher functionals Nourdin, Ivan ; Peccati, Giovanni ; in Electronic Journal of Probability (2010), 15 Detailed reference viewed: 103 (2 UL) |
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