An explicit Fredholm determinant formula is derived for the multipoint distribution of the
height function of the totally asymmetric simple exclusion process (TASEP) with arbitrary …

We consider the colored asymmetric simple exclusion process (ASEP) and stochastic six
vertex (S6V) model with fully packed initial conditions; the states of these models can be …

In this text we introduce and analyze families of symmetric functions arising as partition
functions for colored fermionic vertex models associated with the quantized affine Lie …

Recently, there has been much progress in understanding stationary measures for colored
(also called multi-species or multi-type) interacting particle systems, motivated by asymptotic …

For models in the KPZ universality class, such as the zero temperature model of planar last
passage-percolation (LPP) and the positive temperature model of directed polymers, its …

We study the multitime distribution in a discrete polynuclear growth model or, equivalently, in
directed last‐passage percolation with geometric weights. A formula for the joint multitime …

This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP)
on a segment of length N. Our main result is that for particle densities in (0, 1), the total …

We discover a new property of the stochastic colored six-vertex model called flip-invariance.
We use it to show that for a given collection of observables of the model, any transformation …

We propose a general method to produce orthogonal polynomial dualities from the∗-
bialgebra structure of Drinfeld–Jimbo quantum groups. The∗-structure allows for the …

These lecture notes, adapted from the habilitation thesis of the author, survey in a first part
various exact results obtained in the past few decades about KPZ fluctuations in one …