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arXiv · 2011.10161

Limit shape of perfect matchings on contracting bipartite graphs

Zhongyang Li
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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.

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Zhongyang Li. 2020-11-20. Limit shape of perfect matchings on contracting bipartite graphs. https://arxiv.org/abs/2011.10161

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