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 …

Over the past 25 years, there has been an explosion of interest in the area of random tilings.
The first book devoted to the topic, this timely text describes the mathematical theory of …

We revisit the problem of determining the Arctic curve in the six-vertex model with domain
wall boundary conditions. We describe an alternative method, by which we recover the …

The parabolic Airy line ensemble AA is a central limit object in the KPZ (Kardar–Parisi–
Zhang) universality class and related areas. On any compact set K= 1,⋯, k× a, a+ t …

These are lecture notes for a mini-course given at the Cornell Probability Summer School in
July 2013. Topics include lozenge tilings of polygons and their representation theoretic …

We study large-scale height fluctuations of random stepped surfaces corresponding to
uniformly random lozenge tilings of polygons on the triangular lattice. For a class of …

We introduce and study stochastic N N-particle ensembles which are discretizations for
general-β β log-gases of random matrix theory. The examples include random tilings …

We develop a new method for studying the asymptotics of symmetric polynomials of
representation-theoretic origin as the number of variables tends to infinity. Several …

Random domino tilings of the Aztec diamond shape exhibit interesting features and some of
the statistical properties seen in random matrix theory. As a statistical mechanical model it …

We consider asymptotics of a domino tiling model on a class of domains which we call
rectangular Aztec diamonds. We prove the Law of Large Numbers for the corresponding …