Work

Correlations in the multispecies TASEP and a conjecture by Lam

Year: 2015

Type: article

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 ~ n − 1 \tilde A_{n-1} and (b) the asymptotic shape of a random integer partition with no hooks of length n n , a so called n 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.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/tran/6806

Authors: Arvind Ayyer, Svante Linusson

Institutions: Indian Institute of Science Bangalore, KTH Royal Institute of Technology

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Department of Science and Technology, Ministry of Science and Technology, India

Award: G3827012654