Asymptotics of two-point correlations in the multi-species q-TAZRP

Abstract

A previous paper by the authors found explicit contour integral formulas for certain joint moments of the multi-species q-TAZRP (totally asymmetric zero range process), using algebraic methods. These contour integral formulas have a "pseudo-factorized" form which makes asymptotic analysis simpler. In this brief note, we use those contour integral formulas to find the asymptotics of the two-point correlations. As expected, the term arising from the "shift-invariance" makes a non-trivial asymptotic contribution.