Reading seminar on integrable probability in Spring 2019

[Spring 2019 semester]

This talk outlines connections between 2-dimensional Gibbs measures with a height function and particle systems in the Kardar-Parisi-Zhang universality class.

[2018/11/15]

We introduce the $q$-Hahn PushTASEP — an integrable stochastic interacting particle system which is a 3-parameter generalization of the PushTASEP, a well-known close relative of the TASEP (Totally Asymmetric Simple Exclusion Process). The transition probabilities in the $q$-Hahn PushTASEP are expressed through the $_4\phi_3$ basic hypergeometric function. Under suitable limits, the $q$-Hahn PushTASEP degenerates to all known integrable (1+1)-dimensional stochastic systems with a pushing mechanism. One can thus view our new system as a pushing counterpart of the $q$-Hahn TASEP introduced by Povolotsky. We establish Markov duality relations and contour integral formulas for the $q$-Hahn PushTASEP. We also take a $q\to1$ limit of our process arriving at a new beta polymer-like model.

Virginia Integrable Probability Summer School will be held
at University of Virginia
from **May 27 to June 8, 2019**

[2018/08/29]

We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems evolve in discrete or continuous space and can be thought of as new exactly solvable examples of tandem queues, directed first- or last-passage percolation models, or Robinson-Schensted-Knuth type systems with random input. One of the features of the particle systems we consider is the presence of spatial inhomogeneity which can lead to the formation of traffic jams.

Workshop on Representation Theory, Combinatorics, and Geometry
will be at University of Virginia on **October 19-21, 2018**. The workshop precedes
the Virginia Mathematics Lectures by Andrei Okounkov (October 22-24)

[Fall 2018 semester]