An illustration of the Gibbs property

Gibbs measures, arctic curves, and random interfaces

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

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The q-Hahn PushTASEP

The q-Hahn PushTASEP

[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.

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Simulation of the six vertex model with domain wall boundary conditions and gaseous phase (simulation due to Shreyas Balaji)

Virginia Integrable Probability Summer School

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

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Emergence of a discontinuity of the height function at a slowdown

Generalizations of TASEP in discrete and continuous inhomogeneous space

[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 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 novel features of the particle systems is the presence of spatial inhomogeneity which can lead to the formation of traffic jams.

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Front of percolation

MATH 3100 • Introduction to Probability (2 sections)

[Fall 2018 semester]

2019 travel

January

8-10 • Moscow, Russia • Conference “New Frontiers in Representation Theory” dedicated to the 70th birthday of G.I.Olshanski, at SkolTech Center for Advances Studies

31-1 • Minneapolis, MN • University of Minnesota

February

27-1 • Manhattan and Lawrence, KS • Kansas State University and University of Kansas

March

10-15 • Banff, Alberta, Canada • BIRS Workshop “Asymptotic Algebraic Combinatorics”

May

2-3 • Blacksburg, VA • Virginia Tech

13-14 • Durham, NC • SouthEastern Probability Conference 2019

All 2019 travel »

[quick link] My big BiBTeX file