Correlations in the multispecies tasep and a conjecture by Lam
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
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.
Asymmetric Exclusion Processes, Particle, Profile, Shape
IdentifiersURN: urn:nbn:se:kth:diva-198865DOI: 10.1090/tran/6806ISI: 000388669200014ScopusID: 2-s2.0-84995783968OAI: oai:DiVA.org:kth-198865DiVA: diva2:1061396
FunderSwedish Research Council, 621-2014-4780
QC 201701022017-01-022016-12-222017-01-02Bibliographically approved