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Height Fluctuations of Random Lozenge Tilings Through Nonintersecting Random Walks

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 نشر من قبل Jiaoyang Huang
 تاريخ النشر 2020
  مجال البحث
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 تأليف Jiaoyang Huang




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In this paper we study height fluctuations of random lozenge tilings of polygonal domains on the triangular lattice through nonintersecting Bernoulli random walks. For a large class of polygons which have exactly one horizontal upper boundary edge, we show that these random height functions converge to a Gaussian Free Field as predicted by Kenyon and Okounkov [28]. A key ingredient of our proof is a dynamical version of the discrete loop equations as introduced by Borodin, Guionnet and Gorin [5], which might be of independent interest.



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