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Correlations in the multispecies TASEP and a conjecture by Lam

Authors: Arvind Ayyer and Svante Linusson
Journal: Trans. Amer. Math. Soc. 369 (2017), 1097-1125
MSC (2010): Primary 05A05, 05A17, 20F55, 60K35, 82C22
Published electronically: February 12, 2016
MathSciNet review: 3572266
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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

Svante Linusson
Affiliation: Department of Mathematics, KTH-Royal Institute of Technology, SE-100 44, Stockholm, Sweden

Received by editor(s): May 6, 2014
Received by editor(s) in revised form: February 10, 2015
Published electronically: February 12, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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