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Shuffling algorithm for boxed plane partitions

Borodin, Alexei and Gorin, Vadim (2009) Shuffling algorithm for boxed plane partitions. Advances in Mathematics, 220 (6). pp. 1739-1770. ISSN 0001-8708. https://resolver.caltech.edu/CaltechAUTHORS:20090428-165110014

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Abstract

We introduce discrete time Markov chains that preserve uniform measures on boxed plane partitions. Elementary Markov steps change the size of the box from a×b×c to (a−1)×(b+1)×c or (a+1)×(b−1)×c. Algorithmic realization of each step involves O((a+b)c) operations. One application is an efficient perfect random sampling algorithm for uniformly distributed boxed plane partitions. Trajectories of our Markov chains can be viewed as random point configurations in the three-dimensional lattice. We compute the bulk limits of the correlation functions of the resulting random point process on suitable two-dimensional sections. The limiting correlation functions define a two-dimensional determinantal point processes with certain Gibbs properties.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.aim.2008.11.008DOIArticle
https://arxiv.org/abs/0804.3071arXivDiscussion Paper
Additional Information:© 2008 Elsevier Inc. Received 20 May 2008; accepted 6 November 2008. Communicated by Andrei Zelevinsky; available online 10 December 2008. The first named author (A.B.) was partially supported by the NSF grant DMS-0707163. The second named author (V.G.) was partially supported by RFBR grant 07-01-91209, the Moebius Contest Foundation for Young Scientists and Leonhard Euler’s Fund of Russian Mathematics Support.
Funders:
Funding AgencyGrant Number
NSFDMS-0707163
Russian Foundation for Basic Research07-01-91209
Moebius Contest Foundation for Young ScientistsUNSPECIFIED
Leonhard Euler’s Fund of Russian Mathematics SupportUNSPECIFIED
Subject Keywords:Plane partitions; Determinantal point processes
Issue or Number:6
Record Number:CaltechAUTHORS:20090428-165110014
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20090428-165110014
Official Citation:Alexei Borodin, Vadim Gorin, Shuffling algorithm for boxed plane partitions, Advances in Mathematics, Volume 220, Issue 6, 2009, Pages 1739-1770, ISSN 0001-8708, https://doi.org/10.1016/j.aim.2008.11.008. (http://www.sciencedirect.com/science/article/pii/S0001870808003253)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14106
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:10 Aug 2009 22:53
Last Modified:03 Oct 2019 00:47

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