Random plane partitions with k-periodic weights develop up to k turning points near the vertical boundary, with correlated GUE-corners processes at each point and rational-slope facets between them.
Correlation functions for determinantal processes defined by infinite block Toeplitz minors
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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 \cite{DK}. We strongly believe that also in other concrete cases the double integral formulas are good starting points for asymptotic studies.
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Turning point processes in plane partitions with periodic weights of arbitrary period
Random plane partitions with k-periodic weights develop up to k turning points near the vertical boundary, with correlated GUE-corners processes at each point and rational-slope facets between them.