Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-Avoiding Walks on the UIPQ   We study an annealed model of Uniform Infinite Planar Quadrangulation (UIPQ)
with an infinite two-sided self-avoiding walk (SAW), which can also be
described as the result of glueing together two independent uniform infinite
quadrangulations of the half-plane (UIHPQs). We prove a lower bound on the
displacement of the SAW which, combined with estimates from our previous paper,
shows that the self-avoiding walk is diffusive. As a byproduct this implies
that the volume growth exponent of the lattice in question is $4$ (as is the
case for the standard UIPQ); nevertheless, using our previous work we show its
law to be singular with respect to that of the standard UIPQ, that is -- in the
language of statistical physics -- the fact that disorder holds.

14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: econ
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs