Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A monotonicity property for random walk in a partially random
  environment   We prove a law of large numbers for random walks in certain kinds of i.i.d.
random environments in Z^d that is an extension of a result of Bolthausen,
Sznitman and Zeitouni (2003). We use this result, along with the lace expansion
for self-interacting random walks, to prove a monotonicity result for the first
coordinate of the speed of the random walk under some strong assumptions on the
distribution of the environment.

11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
1
The categories of this paper are: cs
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn