Lyapunov exponents for the simple random walk in random potentials

Thời gian: 14h chiều Thứ 5, ngày  03/09/2026

Địa điểm: Phòng 507 nhà A6

Abstract: We consider the simple random walk in i.i.d. nonnegative random potentials on the d-dimensional integer lattice. In this model, the so-called Lyapunov exponent describes the “cost” paid by the walker for traveling from the origin to a remote location in a landscape of potential. The Lyapunov exponent is related not only to the traveling cost but also to the large deviation principle. In fact, the rate function is expressed in terms of the Lyapunov exponent. Hence, it is important to study the properties of the Lyapunov exponent. In this talk, we review previous work and focus in particular on the comparison between Lyapunov exponents for different laws of the potential.