Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The potential function and ladder variables of a recurrent random walk
  on $\mathbb{Z}$ with infinite variance   We consider a recurrent random walk of i.i.d. increments on the
one-dimensional integer lattice and obtain a formula relating the hitting
distribution of a half-line with the potential function, $a(x)$, of the random
walk. Applying it, we derive an asymptotic estimate of $a(x)$ and thereby a
criterion for $a(x)$ to be bounded on a half-line. The application is also made
to estimate some hitting probabilities as well as to derive asymptotic
behaviour for large times of the walk conditioned never to visit the origin.

0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th