Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak invariance principle for the local times of Gibbs-Markov processes   The subject of this paper is to prove a functional weak invariance principle
for the local time of a process generated by a Gibbs-Markov map. More
precisely, let $\left(X,\mathcal{B},m,T,\alpha\right)$ is a mixing, probability
preserving Gibbs-Markov{\normalsize{}. and let $\varphi\in L^{2}\left(m\right)$
be an aperiodic function with mean $0$. Set $S_{n}=\sum_{k=0}^{n}X_{k}$ and
define the hitting time process $L_{n}\left(x\right)$ be the number of times
$S_{k}$ hits $x\in\mathbb {Z}$ up to step $n.$ The normalized local time
process $l_{n}\left(x\right)$ is defined by $
l_{n}\left(t\right)=\frac{L_{n}\left(\left\lfloor \sqrt{n}x\right\rfloor
\right)}{\sqrt{n}},\,\, x\in\mathbb{R}$.
  We prove under that $l_{n}\left(x\right)$ converges in distribution to the
local time of the Brownian Motion. The proof also applies to the more classical
setting of local times derived from a subshift of finite type endowed with a
Gibbs measure.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph