Tertuliano Franco

UFBA

Local: Auditório do Edifício Antonio Galves (NUMEC)

Horário: 14h00

Heat Equation with Wentzel boundary conditions as a limit of random particle systems

 Resumo: In this talk we consider two interacting particle systems in the finite box with N sites, namely, independent random walks and symmetric exclusion processes. Both systems are in contact with a finite reservoir, where the exit rate is proportional to the inverse of $N^\theta$, where  $\theta$ is nonnegative. We prove the hydrodynamic limit for these models, which are given by the heat equation with Wentzell boundary conditions at the boundary at the critical parameter , and exhibit a dynamic phase transition. Moreover, the Wentzell boundary condition is non-linear in the exclusion setting at the critical parameter $\theta=1$. Joint work with Patrícia Gonçalves and Matheus Franco.

Jhon Astoquillca

IME-USP

Local: Auditório do Edifício Antonio Galves (NUMEC)

Horário: 14h00

Collisions of random walks in unimodular random graphs

 Resumo: We look at collisions of two independent random walks on graphs and how they relate to recurrence and transience. We start by recalling what happens in the bounded-degree setting and why things become more subtle when degrees are unbounded. This leads naturally to unimodularity and the Mass-Transport Principle. We then prove a general criterion for having only finitely many collisions and use it in one concrete example: the supercritical Gilbert random geometric graph. In that setting, we recover the expected dimension-dependent picture: infinitely many collisions in dimension two and only finitely many in dimensions three and higher.