Joint $q$moments and shift invariance for the multispecies $q$TAZRP on the infinite line
Abstract
This paper presents a novel method for computing certain particle locations in the multispecies $q$TAZRP (totally asymmetric zero range process). The method is based on a decomposition of the process into its discretetime embedded Markov chain, which is described more generally as a monotone process on a graded partially ordered set; and an independent family of exponential random variables. A further ingredient is explicit contour integral formulas for the transition probabilities of the $q$TAZRP. The main result of this method is a shift invariance for the multispecies $q$TAZRP on the infinite line. By a previously known Markov duality result, these particle locations are the same as joint $q$moments. One particular special case is that for step initial conditions, ordered multipoint joint $q$moments of the $n$species $q$TAZRP match the $n$point joint $q$moments of the singlespecies $q$TAZRP. Thus, we conjecture that the Airy$_2$ process describes the joint multipoint fluctuations of multispecies $q$TAZRP. As a probabilistic application of this result, we find explicit contour integral formulas for the joint $q$moments of the multispecies $q$TAZRP in the diffusive scaling regime.
 Publication:

arXiv eprints
 Pub Date:
 March 2022
 DOI:
 10.48550/arXiv.2203.06713
 arXiv:
 arXiv:2203.06713
 Bibcode:
 2022arXiv220306713K
 Keywords:

 Mathematics  Probability;
 Mathematics  Combinatorics
 EPrint:
 version 2 adds a probabilistic application of the main result