Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of graphs with sub exponential transitions probability decay
  and applications   In this paper, we present a complete proof of the construction of graphs with
bounded valency such that the simple random walk has a return probability at
time $n$ at the origin of order $exp(-n^{\alpha}),$ for fixed $\alpha \in
[0,1[$ and with Folner function $exp(n^{\frac{2\alpha}{1-\alpha}})$. We begin
by giving a more detailled proof of this result contained in (see
\cite{ershdur}). In the second part, we give an application of the existence of
such graphs. We obtain bounds of the correct order for some functional of the
local time of a simple random walk on an infinite cluster on the percolation
model.

34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio