Planar $3$-webs and the boundary measurement matrix
Probability
2023-12-25 v1 Mathematical Physics
math.MP
Abstract
We compute connection probabilities for reduced -webs in the triple-dimer model on circular planar graphs using the boundary measurement matrix (reduced Kasteleyn matrix). As one application we compute several " generalizations'' of the Lindstr{\o}m-Gessel-Viennot theorem, for "parallel" webs and for honeycomb webs. We also apply our results to the scaling limit of the dimer model in a planar domain, giving conformally invariant expressions for reduced web probabilities.
Keywords
Cite
@article{arxiv.2312.14761,
title = {Planar $3$-webs and the boundary measurement matrix},
author = {Richard Kenyon and Haolin Shi},
journal= {arXiv preprint arXiv:2312.14761},
year = {2023}
}