We prove that the Itô map, that is the map that gives the solution of a differential equation controlled by a rough path of finite $p$-variation with $p\in [2,3)$ is locally Lipschitz continuous in all its arguments and we give…

We consider a coalescent process as a model for the genealogy of a sample from a population. The population is subject to neutral mutation at constant rate $\rho$ per individual and every mutation gives rise to a completely new type.…

We consider a superprocess in a random environment represented by a random measure which is white in time and colored in space with correlation kernel $g(x,y)$. Suppose that $g(x,y)$ decays at a rate of $|x-y|^{-\alpha}$, $0\leq \alpha\leq 2$, as $|x-y|\to\infty$.…

In the paper [1] two expressions for the so called GUE minor kernel are presented, one in definition 1.2 and one in the the formulas (5.6) and (5.7). The expressions given in (5.6) and (5.7) are correct, but the expression…

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 extend to the matrix setting a recent result of Srivastava-Vershynin about estimating the covariance matrix of a random vector. The result can be interpreted as a quantified version of the law of large numbers for  positive semi-definite matrices which…