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 …

We construct explicit one-parameter families of stationary measures for the Kardar–Parisi–
Zhang equation in half-space with Neumann boundary conditions at the origin, as well as for …

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 …

Macdonald processes are measures on sequences of integer partitions built using the
Cauchy summation identity for Macdonald symmetric functions. These measures are a …

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 …

These lecture notes discuss several related features of the exactly solvable two-dimensional
corner growth model with exponentially distributed weights. A key property of this model is …

The Kardar-Parisi-Zhang (KPZ) equation on the real line is well-known to admit Brownian
motion with a linear drift as a stationary distribution (modulo additive constants). We show …