Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Joint $q$-moments and shift invariance for the multi-species $q$-TAZRP
  on the infinite line   This paper presents a novel method for computing certain particle locations
in the multi-species $q$-TAZRP (totally asymmetric zero range process). The
method is based on a decomposition of the process into its discrete-time
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 multi-species $q$-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 multi-point joint $q$-moments of the $n$-species $q$-TAZRP
match the $n$-point joint $q$-moments of the single-species $q$-TAZRP. Thus, we
conjecture that the Airy$_2$ process describes the joint multi-point
fluctuations of multi-species $q$-TAZRP.

19
The categories of this paper are: eess
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas