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Limit shape of perfect matchings on contracting bipartite graphs

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 نشر من قبل Zhongyang Li
 تاريخ النشر 2020
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 تأليف Zhongyang Li




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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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