Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Liouville Property for Isotropic Diffusions in Random Environment   We obtain a Liouville property for stationary diffusions in random
environment which are small, isotropic perturbations of Brownian motion in
spacial dimension greater than two. Precisely, we prove that, on a subset of
full probability, the constant functions are the only strictly sub-linear maps
which are invariant with respect to the evolution of the diffusion. And, we
prove that the constant functions are the only bounded, ancient maps which are
invariant under the evolution. These results depend upon the previous work of
Fehrman [3] and Sznitman and Zeitouni [7] and, in the first case, our methods
are motivated by the work, in the discrete setting, of Benjamini,
Duminil-Copin, Kozma and Yadin [1].

17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat