Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correlation lengths for random polymer models and for some renewal
  sequences   We consider models of directed polymers interacting with a one-dimensional
defect line on which random charges are placed. More abstractly, one starts
from renewal sequence on $\Z$ and gives a random (site-dependent) reward or
penalty to the occurrence of a renewal at any given point of $\mathbb Z$. These
models are known to undergo a delocalization-localization transition, and the
free energy $\tf$ vanishes when the critical point is approached from the
localized region. We prove that the quenched correlation length $\xi$, defined
as the inverse of the rate of exponential decay of the two-point function, does
not diverge faster than $ 1/\tf$. We prove also an exponentially decaying upper
bound for the disorder-averaged two-point function, with a good control of the
sub-exponential prefactor. We discuss how, in the particular case where
disorder is absent, this result can be seen as a refinement of the classical
renewal theorem, for a specific class of renewal sequences.

4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn