We give a principle of large deviations for a generalized version of the strong central limit theorem. This generalized version deals with martingale additive functionals of a recurrent Markov process.

We study boundary conditions for a stochastic pseudo processes corresponding to the biharmonic operator. The biharmonic pseudo process (BPP for short). is composed, in a sense, of two different particles, a monopole and a dipole. We show how an initial-boundary…

The Fractional Brownian Motion can be extended to complex values of the parameter $\alpha $ for $\Re\alpha >{1\over 2}$. This is a useful tool. Indeed, the obtained process depends holomorphically on the parameter, so that many formulas, as Itô formula,…

Two different problems are studied: For an infinite locally finite connected graph $G$, let $p_c(G)$ be the critical value for the existence of an infinite cluster in iid bond percolation on $G$ and let $P_c = \sup\{p_c(G): G \text{ transitive…

We give an account of some results, both old and new, about any $n\times n$ Markov matrix that is embeddable in a one-parameter Markov semigroup. These include the fact that its eigenvalues must lie in a certain region in the…

We construct and study space homogeneous and isotropic random measures (MMRM) which generalize the so-called MRM measures constructed by previous authors. Our measures satisfy an exact scale invariance equation and are therefore natural models in dimension 3 for the dissipation…

We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component with variance $N^{-3/4+\beta}$ for some positive $\beta>0$. We prove that the local eigenvalue statistics…

We study a one dimensional two-type contact process with equal rate of propagation (and death) of the two types. We show that the progeny of a finite number of mutants has a positive probability of survival if and only at…

We consider the internal diffusion limited aggregation (IDLA) process on the infinite cluster in supercritical Bernoulli bond percolation on $\mathbb{Z}^d$. It is shown that the process on the cluster behaves like it does on the Euclidean lattice, in that the…

We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to analyze both the effective Brownian motion and the effective local time. We prove that the limiting process…