Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A shape theorem and a variational formula for the quenched Lyapunov
  exponent of random walk in a random potential   We prove a shape theorem and derive a variational formula for the limiting
quenched Lyapunov exponent and the Green's function of random walk in a random
potential on a square lattice of arbitrary dimension and with an arbitrary
finite set of steps. The potential is a function of a stationary environment
and the step of the walk. This potential is subject to a moment assumption
whose strictness is tied to the mixing of the environment. Our setting includes
directed and undirected polymers, random walk in static and dynamic random
environment, and, when the temperature is taken to zero, our results also give
a shape theorem and a variational formula for the time constant of both site
and edge directed last-passage percolation and standard first-passage
percolation.

20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph