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Correlations in the multispecies tasep and a conjecture by Lam
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6339-2230
2017 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 369, no 2, 1097-1125 p.Article in journal (Refereed) Published
Abstract [en]

We study correlations in the multispecies TASEP on a ring. Results on the correlation of two adjacent points prove two conjectures by Thomas Lam on (a) the limiting direction of a reduced random walk in (A) over tilde (n-1) and (b) the asymptotic shape of a random integer partition with no hooks of length n, a so called n-core. We further investigate two-point correlations far apart and three-point nearest neighbour correlations and prove explicit formulas in almost all cases. These results can be seen as a finite strengthening of correlations in the TASEP speed process by Amir, Angel and Valko. We also give conjectures for certain higher order nearest neighbour correlations. We find an unexplained independence property (provably for two points, conjecturally for more points) between points that are closer in position than in value that deserves more study.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2017. Vol. 369, no 2, 1097-1125 p.
Keyword [en]
Asymmetric Exclusion Processes, Particle, Profile, Shape
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-198865DOI: 10.1090/tran/6806ISI: 000388669200014ScopusID: 2-s2.0-84995783968OAI: oai:DiVA.org:kth-198865DiVA: diva2:1061396
Funder
Swedish Research Council, 621-2014-4780
Note

QC 20170102

Available from: 2017-01-02 Created: 2016-12-22 Last updated: 2017-01-02Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • modern-language-association-8th-edition
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  • de-DE
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  • en-US
  • fi-FI
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  • nn-NB
  • sv-SE
  • Other locale
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Output format
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