Stochastic higher spin vertex models on the line
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 enjoy certain Markov dualities.
Implementation of Glauber dynamics simulation of random lozenge tilings
I’ve implemented the Glauber dynamics to (approximately) sample uniformly random lozenge tilings of polygons of Gelfand-Tsetlin type. These polygons are called sawtooth domains by J. Novak. This paper by B. Laslier and F.L. Toninelli establishes rate of convergence of the Glauber dynamics to the uniformly random lozenge tiling.
MATH 5110 • Introduction to Stochastic Processes
Spectral theory for interacting particle systems
This talk describes results on spectral theory for q-Hahn zero-range process, ASEP, six-vertex model, and q-TASEP. Based on [14] and [17].
MATH 3100 • Introduction to Probability
Math Club
Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz
We develop spectral theory for the $q$-Hahn stochastic particle system introduced recently by Povolotsky. That is, we establish a Plancherel type isomorphism result which implies completeness and biorthogonality statements for the Bethe ansatz eigenfunctions of the system.
Facts about Markov chains
I have collected a number of facts about Markov chains that were discussed in lectures 5-9 in the graduate probability course in Spring 2014.