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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Correlations in the multispecies TASEP and a conjecture by Lam
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by Arvind Ayyer and Svante Linusson PDF
Trans. Amer. Math. Soc. 369 (2017), 1097-1125 Request permission

Abstract:

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 $\tilde A_{n-1}$ 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 Valkó. 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.

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Additional Information
  • Arvind Ayyer
  • Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
  • Email: arvind@math.iisc.ernet.in
  • Svante Linusson
  • Affiliation: Department of Mathematics, KTH-Royal Institute of Technology, SE-100 44, Stockholm, Sweden
  • MR Author ID: 360616
  • Email: linusson@math.kth.se
  • Received by editor(s): May 6, 2014
  • Received by editor(s) in revised form: February 10, 2015
  • Published electronically: February 12, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 1097-1125
  • MSC (2010): Primary 05A05, 05A17, 20F55, 60K35, 82C22
  • DOI: https://doi.org/10.1090/tran/6806
  • MathSciNet review: 3572266