Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The infinite valley for a recurrent random walk in random environment   We consider a one-dimensional recurrent random walk in random environment
(RWRE). We show that the - suitably centered - empirical distributions of the
RWRE converge weakly to a certain limit law which describes the stationary
distribution of a random walk in an infinite valley. The construction of the
infinite valley goes back to Golosov. As a consequence, we show weak
convergence for both the maximal local time and the self-intersection local
time of the RWRE and also determine the exact constant in the almost sure upper
limit of the maximal local time.

10
The categories of this paper are: q-bio
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph