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

We present the first exact solution for the time-dependent equations of the macroscopic
fluctuation theory (MFT) for the symmetric simple exclusion process by combining a …

The One-Dimensional KPZ Equation and Its Universality Class | SpringerLink Skip to main
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The stochastic partial differential equation proposed nearly three decades ago by Kardar,
Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here …

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 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 …

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 consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant.
For this model we derive concise integral representations for multi-point q-moments of the …

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 …