Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moderate deviations for the range of a transient random walk. II   We obtain sharp upper and lower bounds for the moderate deviations of the
volume of the range of a random walk in dimension five and larger. Our results
encompass two regimes: a Gaussian regime for small deviations, and a stretched
exponential regime for larger deviations. In the latter regime, we show that
conditioned on the moderate deviations event, the walk folds a small part of
its range in a ball-like subset. Also, we provide new path properties, in
dimension three as well. Besides the key role Newtonian capacity plays in this
study, we introduce two original ideas, of general interest, which strengthen
the approach developed in \cite{AS}.

32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ