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Variants of geometric RSK, geometric PNG, and the multipoint distribution of the log-gamma polymer
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Nguyen, Vu-Lan and Zygouras, Nikos (2016) Variants of geometric RSK, geometric PNG, and the multipoint distribution of the log-gamma polymer. International Mathematics Research Notices . rnw145. doi:10.1093/imrn/rnw145 ISSN 1073-7928.
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Official URL: http://dx.doi.org/10.1093/imrn/rnw145
Abstract
We show that the reformulation of the geometric Robinson-Schensted-Knuth (gRSK) correspondence via local moves, introduced in \cite{OSZ14} can be extended to cases where the input matrix is replaced by more general polygonal, Young-diagram-like, arrays of the form $\polygon$. We also show that a rearrangement of the sequence of the local moves gives rise to a geometric version of the polynuclear growth model (PNG). 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 N and space at distance of order N2/3, we show formally that the joint law of the partition functions, scaled by N1/3, converges to the two-point function of the Airy process
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | International Mathematics Research Notices | ||||
Publisher: | Oxford University Press | ||||
ISSN: | 1073-7928 | ||||
Official Date: | 2016 | ||||
Dates: |
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Article Number: | rnw145 | ||||
DOI: | 10.1093/imrn/rnw145 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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