Brownian motion is a continuum scaling limit for a wide class of random processes, and
there has been great success in developing a theory for its properties (such as distribution …

Macdonald processes are probability measures on sequences of partitions defined in terms
of nonnegative specializations of the Macdonald symmetric functions and two Macdonald …

This unique book provides the first introduction to crystal base theory from the combinatorial
point of view. Crystal base theory was developed by Kashiwara and Lusztig from the …

We construct a family of stochastic growth models in 2+ 1 dimensions, that belong to the
anisotropic KPZ class. Appropriate projections of these models yield 1+ 1 dimensional …

We introduce a four-parameter family of interacting particle systems on the line, which can
be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which …

We consider two models for directed polymers in space‐time independent random media
(the O'Connell‐Yor semidiscrete directed polymer and the continuum directed random …

We prove that the stationary measures for the free-energy increment process for the
geometric last passage percolation (LPP) and log-gamma polymer model on a diagonal …

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 compute the one-point probability distribution for the stationary KPZ equation (ie initial
data H (0, X)= B (X) H(0,X)=B(X), for B (X) a two-sided standard Brownian motion) and show …

We prove that under n 1/3 scaling, the limiting distribution as n→∞ of the free energy of
Seppäläinen's log-Gamma discrete directed polymer is GUE Tracy-Widom. The main …