Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence parameters of nonnegative block tri-diagonal matrices and
  their application to multi-dimensional QBD processes   First, we consider a nonnegative homogeneous block tri-diagonal matrix and
obtain its convergence parameter, where some results in the field of matrix
analytic method are extended to the case where block matrices have countably
infinite dimension. Second, we apply our results to a multi-dimensional QBD
process and obtain lower bounds for the directional asymptotic decay rates of
the stationary distribution.

12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys