Correlation functions for determinantal processes defined by infinite block Toeplitz minors

2019/01/30 by Tomas Berggren, Berggren, T., Maurice Duits +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1901.10877

openalex publication_date 2019/01/30 · openalex created_date 2019/03/02 · openalex updated_date 2026/07/28

Abstract

We study the correlation functions for determinantal point processes defined by products of infinite minors of block Toeplitz matrices. The motivation for studying such processes comes from doubly periodically weighted tilings of planar domains, such as the two-periodic Aztec diamond. Our main results are double integral formulas for the correlation kernels. In general, the integrand is a matrix-valued function built out of a factorization of the matrix-valued weight. In concrete examples the factorization can be worked out in detail and we obtain explicit integrands. In particular, we find an alternative proof for a formula for the two-periodic Aztec diamond recently derived in \citeDK. We strongly believe that also in other concrete cases the double integral formulas are good starting points for asymptotic studies.

Citations

• Infinite wedge and random partitions

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