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Correlation functions for determinantal processes defined by infinite block Toeplitz minors
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7598-4521
2019 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 356, article id 106766Article in journal (Refereed) Published
Abstract [en]

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 [20]. We strongly believe that also in other concrete cases the double integral formulas are good starting points for asymptotic studies.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2019. Vol. 356, article id 106766
Keywords [en]
Determinantal point processes, Non-negative block Toeplitz minors, Non-intersecting paths, Periodically weighted random tilings
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-263330DOI: 10.1016/j.aim.2019.106766ISI: 000491211800001Scopus ID: 2-s2.0-85071414409OAI: oai:DiVA.org:kth-263330DiVA, id: diva2:1375924
Note

QC 20191206

Available from: 2019-12-06 Created: 2019-12-06 Last updated: 2019-12-06Bibliographically approved

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Berggren, TomasDuits, Maurice

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