Glauco Valle

Convergence to the Brownian Web for a generalization of the drainage network model

We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing crossing paths and exibiting dependence before coalescence. We show that under diffusive scaling this system converges in distribution to the Brownian Web.

A microscopic model for Stefan's melting and freezing problem

We study a class of one-dimensional interacting particle systems with random boundaries as a microscopic model for Stefans melting and freezing problem. We prove that under diffusive rescaling these particle systems exhibit a hydrodynamic behavior described by the solution of a Cauchy-Stefan problem.

SPECTRUM OF STOCHASTIC ADDING MACHINES AND FIBERED JULIA SETS

Consider the basic algorithm to perform the transformation n ↦ n + 1 changing digits of the d-adic expansion of n one by one. We obtain a family of Markov chains on the non-negative integers through successive and independent applications of the algorithm modified by a parametrized stochastic rule that randomly prevents one of the steps in the algorithm to finish. The objects of study in this paper are the spectra of the transition operators of these Markov chains. The spectra of these Markov chains turn out to be fibered Julia sets of fibered polynomials. This enables us to analyze their topological and analytical properties with respect to the underlying parameters of the Markov chains.

On the copula for multivariate extreme value distributions

We show that all multivariate Extreme Value distributions, which are the possible weak limits of the

Exponential Convergence for the Fredrickson–Andersen One-Spin Facilitated Model

K

Convergence Results and Sharp Estimates for the Voter Model Interfaces

largest order statistics of iid sequences, have the same copula, the so called K-extremal copula. This copula is described through exact expressions for its density and distribution functions. We also study measures of dependence, we obtain a weak convergence result and we propose a simulation algorithm for the K-extremal copula.

On the Speed of the One-dimensional Excited Random Walk in the Transient Regime

We prove exponential convergence to equilibrium for the Fredrickson–Andersen one-spin facilitated model on bounded degree graphs satisfying a subexponential, but larger than polynomial, growth condition. This was a classical conjecture related to non-attractive spin systems. Our proof relies on coupling techniques based on Harris graphical construction for interacting particle systems.