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On the domino shuffle and matrix refactorizations

Chhita, Sunil; Duits, Maurice

On the domino shuffle and matrix refactorizations Thumbnail


Maurice Duits


This paper is motivated by computing correlations for domino tilings of the Aztec diamond. It is inspired by two of the three distinct methods that have recently been used in the simplest case of a doubly periodic weighting, that is, the two-periodic Aztec diamond. One of the methods, powered by the domino shuffle, involves inverting the Kasteleyn matrix giving correlations through the local statistics formula. Another of the methods, driven by a Wiener–Hopf factorization for two-by-two matrix-valued functions, involves the Eynard–Mehta Theorem. For arbitrary weights, the Wiener–Hopf factorization can be replaced by an LU- and UL-decomposition, based on a matrix refactorization, for the product of the transition matrices. This paper shows that, for arbitrary weightings of the Aztec diamond, the evolution of the face weights under the domino shuffle and the matrix refactorization is the same. In particular, these dynamics can be used to find the inverse of the LGV matrix in the Eynard–Mehta Theorem.


Chhita, S., & Duits, M. (2023). On the domino shuffle and matrix refactorizations. Communications in Mathematical Physics, 401(2), 1417-1467.

Journal Article Type Article
Acceptance Date Feb 3, 2023
Online Publication Date Apr 6, 2023
Publication Date 2023-07
Deposit Date Feb 13, 2023
Publicly Available Date Jul 5, 2023
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 401
Issue 2
Pages 1417-1467
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