The multitiling model

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February 25, 2021
10:20AM - 11:15AM
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Zoom

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Add to Calendar 2021-02-25 10:20:00 2021-02-25 11:15:00 The multitiling model Speaker:  Richard Kenyon (Yale University) Title:  The multitiling model Abstract:  The study of random tilings is a cornerstone area of combinatorics and probability. Unfortunately the tiling problem is NP-hard even in quite simple-looking cases. We study a tractable variant, the multitiling model, where we tile a region with high multiplicity. In the limit of large multiplicities we compute the asymptotic growth rate of the number of multitilings: the free energy of the multitiling model. We show that the individual tile densities tend to a Gaussian field with respect to an associated discrete Laplacian. For tilings with translates of a polyomino on Z^2 we find crystallization phenomena (and accompanying phase transitions), and even naturally occurring quasicrystals. This is joint work with Andrei Pohoata (Yale). Zoom Department of Mathematics math@osu.edu America/New_York public
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Speaker:  Richard Kenyon (Yale University)

Title:  The multitiling model

Abstract:  The study of random tilings is a cornerstone area of combinatorics and probability. Unfortunately the tiling problem is NP-hard even in quite simple-looking cases. We study a tractable variant, the multitiling model, where we tile a region with high multiplicity. In the limit of large multiplicities we compute the asymptotic growth rate of the number of multitilings: the free energy of the multitiling model. We show that the individual tile densities tend to a Gaussian field with respect to an associated discrete Laplacian. For tilings with translates of a polyomino on Z^2 we find crystallization phenomena (and accompanying phase transitions), and even naturally occurring quasicrystals.

This is joint work with Andrei Pohoata (Yale).

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