This is an introductory course on the methods of computing asymptotics of probabilities of
rare events: the theory of large deviations. The book combines large deviation theory with …

This monograph contains the notes of lectures I gave in Saint Flour Probability Summer
School in July 2016. The two other courses were given by Paul Bourgade and by Scott …

We introduce an exactly-solvable model of random walk in random environment that we call
the Beta RWRE. This is a random walk in ZZ which performs nearest neighbour jumps with …

Probabilistic models of directed polymers in random environment have received
considerable attention in recent years. Much of this attention has focused on integrable …

The first goal of this paper is to prove multiple asymptotic results for a time‐discrete and
space‐continuous polymer model of a random walk in a random potential. These results …

We study the directed last-passage percolation model on the planar square lattice with
nearest-neighbor steps and general iid weights on the vertices, outside of the class of …

We study the directed last-passage percolation model on the planar integer lattice with
nearest-neighbor steps and general iid weights on the vertices, outside the class of exactly …

The first-passage time for a single diffusing particle has been studied extensively, but the
first-passage time of a system of many diffusing particles, as is often the case in physical …

We consider the homogenization of Hamilton–Jacobi equations and degenerate Bellman
equations in stationary, ergodic, unbounded environments. We prove that, as the …

We consider random walk in a space-time random potential, also known as directed random
polymer measures, on the planar square lattice with nearest-neighbor steps and general iid …