Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An expansion for self-interacting random walks   We derive a perturbation expansion for general self-interacting random walks,
where steps are made on the basis of the history of the path. Examples of
models where this expansion applies are reinforced random walk, excited random
walk, the true (weakly) self-avoiding walk, loop-erased random walk, and
annealed random walk in random environment.
  In this paper we show that the expansion gives rise to useful formulae for
the speed and variance of the random walk, when these quantities are known to
exist. The results and formulae of this paper have been used elsewhere by the
authors to prove monotonicity properties for the speed (in high dimensions) of
excited random walk and related models, and certain models of random walk in
random environment.
  We also derive a law of large numbers and central limit theorem (with
explicit error terms) directly from this expansion, under strong assumptions on
the expansion coefficients. The assumptions are shown to be satisfied by
excited random walk in high dimensions with small excitation parameter, a model
of reinforced random walk with underlying drift and small reinforcement
parameter, and certain models of random walk in random environment under strong
ellipticity conditions. This is the extended version of the paper, where we
provide all proofs.

23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph