Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Walk on a Surface Group: Boundary Behavior of the Green's
  Function at the Spectral Radius   It is proved that the Green's function of the simple random walk on a surface
group of large genus decays exponentially at the spectral radius. It is also
shown that Ancona's inequalities extend to the spectral radius R, and therefore
that the Martin boundary for R-potentials coincides with the natural geometric
boundary S^1. This implies that the Green's function obeys a power law with
exponent 1/2 at the spectral radius.

36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio