Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic orders and the frog model   The frog model starts with one active particle at the root of a graph and
some number of dormant particles at all nonroot vertices. Active particles
follow independent random paths, waking all inactive particles they encounter.
We prove that certain frog model statistics are monotone in the initial
configuration for two nonstandard stochastic dominance relations: the
increasing concave and the probability generating function orders.
  This extends many canonical theorems. We connect recurrence for random
initial configurations to recurrence for deterministic configurations. Also,
the limiting shape of activated sites on the integer lattice respects both of
these orders. Other implications include monotonicity results on transience of
the frog model where the number of frogs per vertex decays away from the
origin, on survival of the frog model with death, and on the time to visit a
given vertex in any frog model.

5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin