Título: Random walk in a birth-and-death dynamical environment

Palestrante: Luiz Renato Fontes (Universidade de São Paulo)
Data: 27/10/2021
Horário: 13:00hrs
Local: Transmissão online

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ID da reunião: 958 0581 3232

Resumo: We consider a particle moving in continuous time as a Markov jump process; its discrete chain given by an ordinary random walk on Z^d (with finite second moments), and its jump rate at (x,t) given by a fixed function f of the state of a simple birth-and-death (BD) process at x on time t. BD processes at different sites are independent and identically distributed, and f is assumed non increasing and vanishing at infinity. We present an argument to obtain a CLT for the particle position when the environment is ergodic. In the absence of a viable uniform lower bound for the jump rate, we resort instead to stochastic domination, as well as to a subadditive argument to control the time spent by the particle to give n jumps (both ingredients rely on the monotonicity of f); and we also impose conditions on the initial (product) environmental initial distribution. We also discuss the asymptotic form of the environment seen by the particle. Joint work with Maicon Pinheiro and Pablo Gomes.