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Permutations with fixed pattern densities
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Kenyon, Robert V., Králʼ, Daniel, Radin, C. and Winkler, P. (2020) Permutations with fixed pattern densities. Random Structures and Algorithms, 56 (1). pp. 220-250. doi:10.1002/rsa.20882 ISSN 1042-9832.
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Official URL: https://doi.org/10.1002/rsa.20882
Abstract
We study scaling limits of random permutations (“permutons”) constrained by having fixed densities of a finite number of patterns. We show that the limit shapes are determined by maximizing entropy over permutons with those constraints. In particular, we compute (exactly or numerically) the limit shapes with fixed 12 density, with fixed 12 and 123 densities, with fixed 12 density and the sum of 123 and 213 densities, and with fixed 123 and 321 densities. In the last case we explore a particular phase transition. To obtain our results, we also provide a description of permutons using a dynamic construction.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Random Structures and Algorithms | ||||||||
Publisher: | John Wiley & Sons, Inc. | ||||||||
ISSN: | 1042-9832 | ||||||||
Official Date: | January 2020 | ||||||||
Dates: |
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Volume: | 56 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 220-250 | ||||||||
DOI: | 10.1002/rsa.20882 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | "This is the peer reviewed version of the following article:Kenyon, R, Král', D, Radin, C, Winkler, P. Permutations with fixed pattern densities. Random Struct Alg. 2019; 1– 31. which has been published in final form at https://doi.org/10.1002/rsa.20882. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions." | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 13 March 2019 | ||||||||
Date of first compliant Open Access: | 31 July 2020 | ||||||||
RIOXX Funder/Project Grant: |
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