Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior of edge-reinforced random walks   In this article, we study linearly edge-reinforced random walk on general
multi-level ladders for large initial edge weights. For infinite ladders, we
show that the process can be represented as a random walk in a random
environment, given by random weights on the edges. The edge weights decay
exponentially in space. The process converges to a stationary process. We
provide asymptotic bounds for the range of the random walker up to a given
time, showing that it localizes much more than an ordinary random walker. The
random environment is described in terms of an infinite-volume Gibbs measure.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin