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Schur dynamics of the Schur processes

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arxiv 1001.3442 v1 pith:IRSAFSGW submitted 2010-01-20 math.CO math-phmath.MPmath.PR

Alexei Borodin This is my paper · ORCID
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We construct discrete time Markov chains that preserve the class of Schur processes on partitions and signatures. One application is a simple exact sampling algorithm for q^{volume}-distributed skew plane partitions with an arbitrary back wall. Another application is a construction of Markov chains on infinite Gelfand-Tsetlin schemes that represent deterministic flows on the space of extreme characters of the infinite-dimensional unitary group.

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  1. Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions

    math.PR 2025-07 conditional novelty 7.0 of 10

    For Aztec diamond tilings with i.i.d. one-periodic edge weights, height function fluctuations are, in the critical regime, GFF plus independent Brownian motion, and in the fixed-variance regime, Brownian motion alone ...

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