Limit shape of perfect matchings on contracting bipartite graphs
Probability
2021-01-07 v2
Abstract
We consider random perfect matchings on a general class of contracting bipartite graphs by letting certain edge weights be 0 on the contracting square-hexagon lattice in a periodic way. We obtain a deterministic limit shape in the scaling limit. The results can also be applied to prove the existence of multiple disconnected liquid regions for all the contracting square-hexagon lattices with certain edge weights, extending the results proved in [13] for contracting square-hexagon lattices where the number of square rows in each period is either 0 or 1.
Keywords
Cite
@article{arxiv.2011.10161,
title = {Limit shape of perfect matchings on contracting bipartite graphs},
author = {Zhongyang Li},
journal= {arXiv preprint arXiv:2011.10161},
year = {2021}
}
Comments
The paper extends results in arXiv:1807.06175 and arXiv:1809.08727