We use the concept of unimodular random graph to show that the branching simple random walk on $\mathbb{Z}^{d}$ indexed by a critical geometric Galton-Watson tree conditioned to survive is recurrent if and only if $d \leq 4$.

Motivated by a generalization of Sturm-Lott-Villani theory to discrete spaces and by a conjecture stated by Shepp and Olkin about the entropy of sums of Bernoulli random variables, we prove the concavity in $t$ of the entropy of the convolution…

We consider continuous-time random interlacements on a transient weighted graph. We prove an identity in law relating the field of occupation times of random interlacements at level u to the Gaussian free field on the weighted graph. This identity is…

Using the linear programming approach to stochastic control introduced by Buckdahn, Goreac, and Quincampoix, and by Goreac and Serea, we provide a semigroup property for some set of probability measures leading to dynamic programming principles for stochastic control problems. An abstract principle is…

We study the Laha-Lukacs property of the free Meixner laws (processes). We prove that some families of free Meixner distribution have the linear regression function. We also show that this families have the property of quadratic conditional variances.

This is an erratum for "Maximal arithemtic progressions in random subsets" appeared in ECP volume 12  paper number 35 (2007), 365-376.

We show that the number of cycles in a random permutation chosen according to generalized Ewens measure is normally distributed and compute asymptotic estimates for the mean and variance.

Upper bounds on characteristic functions are derived in terms of the entropic distance to the class of normal distributions.

We prove that Vertex Reinforced Random Walk on $\mathbb{Z}$ with weight  of order $k^\alpha$, with $\alpha\in [0,1/2)$, is either almost surely recurrent or almost surely transient.  This improves a previous result of Volkov who showed that the set of sites…

With the help of the Gauss-Laplace transform for the exit time from a cone of planar Brownian motion, we obtain some infinite divisibility properties for the reciprocal of this exit time.