Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the statistical physics of directed polymers in a random medium and
  their relation to tree codes   Using well-known results from statistical physics, concerning the almost-sure
behavior of the free energy of directed polymers in a random medium, we prove
that random tree codes achieve the distortion-rate function almost surely under
a certain symmetry condition.

8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn