Abstract:
We study random walks on dynamical random environments in 1 + 1 dimensions. Under a mild mixing assumption on the environment, we establish a law of large numbers for the random walk as well as a concentration inequality around its asymptotic speed. This mixing condition imposes a polynomial decay of covariances with sufficiently high exponent for events supported on space-time boxes separated in time. However, uniform mixing is not required. Examples of environments for which our methods apply include the contact process and Markovian environments with a positive spectral gap, such as the East model. This is a joint work with Augusto Teixeira and Oriane Blondel.
Biography:
Marcelo R. Hilario is a Visiting Assistant Professor at NYU Shanghai. Prior, he was an assistant professor at The Federal University of Minas Gerais (UFMG) in Belo Horizonte, Brazil. He received his Ph.D. in mathematics in 2011 at The Brazilian National Institute for Pure and Applied Mathematics (IMPA), in Rio de Janeiro. His current research concentrates in probability theory and stochastic processes with emphasis in random media, percolation theory and random walks in dynamical random environments. He was a visiting research fellow in the Mathematical Physics group at the University of Geneva in Switzerland from August 2014 to October 2015 under the supervision of Prof. Hugo DuminilCopin.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai