Journal Article

Variants of Geometric RSK, Geometric PNG, and the Multipoint Distribution of the Log-Gamma Polymer

Vu-Lan Nguyen and Nikos Zygouras

in International Mathematics Research Notices

Volume 2017, issue 15, pages 4732-4795
Published in print August 2017 | ISSN: 1073-7928
Published online July 2016 | e-ISSN: 1687-0247 | DOI: https://dx.doi.org/10.1093/imrn/rnw145
Variants of Geometric RSK, Geometric PNG, and the Multipoint Distribution of the Log-Gamma Polymer

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Abstract

We show that the reformulation of the geometric Robinson–Schensted–Knuth correspondence via local moves, introduced in [29], can be extended to cases where the input matrix is replaced by more general polygonal, Young-diagram-like, arrays of the form . We also show that a rearrangement of the sequence of the local moves gives rise to a geometric version of the polynuclear growth model. These reformulations are used to obtain integral formulae for the Laplace transform of the joint distribution of the point-to-point partition functions of the log-gamma polymer at different space–time points. In the case of two points at equal time [math] and space at distance of order [math], we show formally that the joint law of the partition functions, scaled by [math], converges to the two-point function of the Airy process.

Journal Article.  14155 words.  Illustrated.

Subjects: Mathematics ; Pure Mathematics

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