4 papers · 1 filter
Random Lozenge Waterfall: Dimensional Collapse of Gibbs Measures
Alisa Knizel, Leonid Petrov
We investigate the asymptotic behavior of the q-Racah probability measure on lozenge tilings of a hexagon whose side lengths scale linearly with a large parameter , while the pa…
Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions
Alexey Bufetov, Leonid Petrov, Panagiotis Zografos
We study the asymptotic behavior of random domino tilings of the Aztec diamond of size in a random environment, where the environment is a one-periodic sequence of i.i.d. rando…
Colored Interacting Particle Systems on the Ring: Stationary Measures from Yang-Baxter Equation
Amol Aggarwal, Matthew Nicoletti, Leonid Petrov
Recently, there has been much progress in understanding stationary measures for colored (also called multi-species or multi-type) interacting particle systems, motivated by asympto…
Grothendieck Shenanigans: Permutons from pipe dreams via integrable probability
Alejandro H. Morales, Greta Panova, Leonid Petrov +1
We study random permutations arising from reduced pipe dreams. Our main model is motivated by Grothendieck polynomials with parameter arising in K-theory of the flag variety…