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

These are lecture notes for a mini-course given at the St. Petersburg School in Probability
and Statistical Physics in June 2012. Topics include integrable models of random growth …

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 study the influence of particle shape on growth processes at the edges of evaporating
drops. Aqueous suspensions of colloidal particles evaporate on glass slides, and convective …

We prove duality relations for two interacting particle systems: the q-deformed totally
asymmetric simple exclusion process (q-TASEP) and the asymmetric simple exclusion …

Heat flows in 1+ 1 dimensional stochastic environment converge after scaling to the random
geometry described by the directed landscape. In this first part, we show that the O'Connell …

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 …

We study the asymmetric six-vertex model in the quadrant with parameters on the stochastic
line. We show that the random height function of the model converges to an explicit …

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 …

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 …