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We consider a fractional Brownian motion with Hurst parameter strictly between 0 and 1. We are interested in the asymptotic behaviour of functionals of the increments of this and related processes and we propose several probabilistic and statistical applications.

Stochastic partial differential equations of divergence form with discontinuous and unbounded coefficients are considered in $C^1$ domains. Existence and uniqueness results are given in weighted $L_p$ spaces, and Holder type estimates are presented.

The Green function of a transient symmetric Markov process can be interpreted as the covariance of a centered Gaussian process. This relation leads to several fruitful identities in law. Symmetric Markov processes and their associated Gaussian process both benefit from…

If $P_t$ is the semigroup associated with the Kawasaki dynamics on $Z^d$ and $f$ is a local function on the configuration space, then the variance with respect to the invariant measure $\mu$ of $P_t f$ goes to zero as $t\to…

We bound the probability that a continuous time simple random walk on the infinite percolation cluster on $Z^d$ returns to the origin at time $t$. We use this result to show that in dimensions 5 and higher the uniform spanning…

We consider the time for a critical nearest particle system, starting in equilibrium subject to possessing a large gap, to achieve equilibrium.

Let $\mu$ be an infinitely divisible law on the real line, $\Lambda(\mu)$ its freely infinitely divisible image by the Bercovici-Pata bijection. The purpose of this article is to produce a new kind of random matrices with distribution $\mu$ at dimension…

We are interested in the asymptotic analysis of the binary search tree (BST) under the random permutation model. Via an embedding in a continuous time model, we get new results, in particular the asymptotic behavior of the profile.

In this paper we prove that in the high temperature region of the Sherrington-Kirkpatrick model for a typical realization of the disorder the weighted average of spins $\sum_{i \leq N} t_i \sigma_i$ will be approximately Gaussian provided that $\max_{i \leq…