2 citations · 4 across the 11 of their papers we have counts for
12 papers
Fluctuations for the Toda lattice
Amol Aggarwal, Matthew Nicoletti
In this paper we consider the Toda lattice at thermal equilibrium, meaning that its variables and are independent Gaussi…
Perfect t-embeddings of doubly periodic Aztec diamonds
Tomas Berggren, Matthew Nicoletti, Marianna Russkikh
We study the large-scale geometry of t-surfaces -- pairs of perfect t-embeddings and their associated origami maps -- arising from dimer models on Aztec diamonds with periodic edge…
Temperleyan Domino Tilings with Holes
Matthew Nicoletti
We analyze asymptotic height function fluctuations in uniformly random domino tiling models on multiply connected Temperleyan domains. Starting from asymptotic formulas derived by…
Gaussian Free Field and Discrete Gaussians in Periodic Dimer Models
Tomas Berggren, Matthew Nicoletti
We analyze height fluctuations in Aztec diamond dimer models with nearly arbitrary periodic edge weights. We show that the centered height function approximates the sum of two inde…
Perfect t-embeddings and Lozenge Tilings
Tomas Berggren, Matthew Nicoletti, Marianna Russkikh
We construct perfect t-embeddings for regular hexagons of the hexagonal lattice, providing the first example, and hence proving existence, for graphs with an outer face of degree g…
Six-Vertex Model and Random Matrix Distributions
Vadim Gorin, Matthew Nicoletti
We survey the connections between the six-vertex (square ice) model of 2d statistical mechanics and random matrix theory. We highlight the same universal probability distributions…
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…
Shuffling algorithm for coupled tilings of the Aztec diamond
David Keating, Matthew Nicoletti
In this article we define a generalization of the domino shuffling algorithm for tilings of the Aztec diamond to the interacting -tilings recently introduced by S. Corteel, A. G…
Perfect t-embeddings of uniformly weighted Aztec diamonds and tower graphs
Tomas Berggren, Matthew Nicoletti, Marianna Russkikh
In this work we study a sequence of perfect t-embeddings of uniformly weighted Aztec diamonds. We show that these perfect t-embeddings can be used to prove convergence of gradients…
Local Statistics and Shuffling for Dimers on a Square-Hexagon Lattice
Matthew Nicoletti
We study the dimer model on special subgraphs of the square hexagon lattice called "tower graphs" of size . Using integrable probability techniques, we confirm that as $N \right…
Irreversible Markov Dynamics and Hydrodynamics for KPZ States in the Stochastic Six Vertex Model
Matthew Nicoletti, Leonid Petrov
We introduce a family of Markov growth processes on discrete height functions defined on the 2-dimensional square lattice. Each height function corresponds to a configuration of th…
Arctic curves phenomena for bounded lecture hall Tableaux
Sylvie Corteel, David Keating, Matthew Nicoletti
Recently the first author and Jang Soo Kim introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. They then enumerated bounded lecture hall ta…