English

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