Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Capacity of the range in dimension 5   We prove a Central limit theorem for the capacity of the range of a symmetric
random walk on $\mathbb Z^5$, under only a moment condition on the step
distribution. The result is analogous to the central limit theorem for the size
of the range in dimension three, obtained by Jain and Pruitt in 1971. In
particular an atypical logarithmic correction appears in the scaling of the
variance. The proof is based on new asymptotic estimates, which hold in any
dimension $d\ge 5$, for the probability that the ranges of two independent
random walks intersect. The latter are then used for computing covariances of
some intersection events, at the leading order.

5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph