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CORRELATIONS IN THE MULTISPECIES TASEP AND A CONJECTURE BY LAM

Ayyer, Arvind and Linusson, Svante (2017) CORRELATIONS IN THE MULTISPECIES TASEP AND A CONJECTURE BY LAM. In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 369 (2). pp. 1097-1125.

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Official URL: http://dx.doi.org/10.1090/tran/6806

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 (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.

Item Type: Journal Article
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Additional Information: Copy right for this article belongs to the AMER MATHEMATICAL SOC, 201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 04 Jan 2017 04:41
Last Modified: 04 Jan 2017 04:41
URI: http://eprints.iisc.ernet.in/id/eprint/55696

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