Edge Effects on Local Statistics in Lattice Dimers: A Study of the Aztec Diamond (Finite Case)

2000/07/22 by H. A. Helfgott, Harald Helfgott, Helfgott, Harald · 1 citation
Mathematics · Physics and Astronomy · #05A15 #05C30 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.CO #math.MP #msc:05A15 #msc:05C30

paper · pdf · doi:10.48550/arxiv.math/0007136

41 pages, 28 figures

arxiv created 2000/07/22 · openalex publication_date 2000/07/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the probability of any local pattern at an arbitrary position in a random dimer configuration in a square grid with an Aztec-diamond boundary.

Cited by

• The 1/4-phenomenon of placement probabilities of tilings in the Aztec diamond

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