Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random walks in the quarter plane with zero drift: an explicit criterion
  for the finiteness of the associated group   In many recent studies on random walks with small jumps in the quarter plane,
it has been noticed that the so-called "group" of the walk governs the behavior
of a number of quantities, in particular through its "order". In this paper,
when the "drift" of the random walk is equal to 0, we provide an effective
criterion giving the order of this group. More generally, we also show that in
all cases where the "genus" of the algebraic curve defined by the kernel is 0,
the group is infinite, except precisely for the zero drift case, where
finiteness is quite possible.

3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci