In [Stochastc Process. Appl., 122(9):3173-3208], the author proved the existence and the uniqueness of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition when the generator and the terminal condition are locally Lipschitz. In this paper, we prove that…

We obtain estimates on the exponential rate of decay of the relative entropy from equilibrium for Markov processes with a non-local infinitesimal generator. We adapt some of the ideas coming from the Bakry-Emery approach to this setting. In particular, we…

We investigate stochastic differential equations with jumps and irregular coefficients, and obtain the existence and uniqueness ofgeneralized stochastic flows. Moreover, we also prove the existence and uniqueness of $L^p$-solutions or measure-valued solutionsfor second order integro-differential equation of Fokker-Planck type.

In previous works, we have developed a new Malliavin calculus on the Poisson space based on the lent particle formula. The aim of this work is to prove that, on the Wiener space for the standard Ornstein-Uhlenbeck structure, we also…

Non-Gaussian concentration estimates are obtained for invariant probability measures of reversible Markov processes. We show that the functional inequalities approach combined with a suitable Lyapunov condition allows us to circumvent the classical Lipschitz assumption of the observables. Our method is general…

We study coupled random walks in the plane such that, at each step, the walks change direction by a uniform random angle plus an extra deterministic angle $\theta$. We compute the Hausdorff dimension of the $\theta$ for which the walk…

This paper describes a second order perturbation analysis of the BK property in the space of Hermitean determinantal probability measures around the subspace of product measures, showing that the second order Taylor approximation of the BK inequality holds for increasing…

We derive Donsker-Vardhan type results for functionals of the occupation times when the underlying random walk on $\mathbb Z^d$ is in the domain of attraction of an operator stable law on $\mathbb R^d$. Applications to random walks on wreath products (also known…

The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd p. We establish the…

We prove an almost sure central limit theorem (CLT) for spatial  extension of stretched (meaning subject to a non-zero pulling force) polymers at very weak disorder in all dimensions $d+1\geq 4$.