Height Fluctuations of Random Lozenge Tilings Through Nonintersecting Random Walks
Probability
2020-11-04 v1 Combinatorics
Abstract
In this paper we study height fluctuations of random lozenge tilings of polygonal domains on the triangular lattice through nonintersecting Bernoulli random walks. For a large class of polygons which have exactly one horizontal upper boundary edge, we show that these random height functions converge to a Gaussian Free Field as predicted by Kenyon and Okounkov [28]. A key ingredient of our proof is a dynamical version of the discrete loop equations as introduced by Borodin, Guionnet and Gorin [5], which might be of independent interest.
Cite
@article{arxiv.2011.01751,
title = {Height Fluctuations of Random Lozenge Tilings Through Nonintersecting Random Walks},
author = {Jiaoyang Huang},
journal= {arXiv preprint arXiv:2011.01751},
year = {2020}
}
Comments
70 pages, 10 figures. Draft version, comments are welcome!