Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large deviations for the local fluctuations of random walks and new
  insights into the "randomness" of Pi   We establish large deviations properties valid for almost every sample path
of a class of stationary mixing processes $(X_1,..., X_n,...)$. These
properties are inherited from those of $S_n=\sum_{i=1}^nX_i$ and describe how
the local fluctuations of almost every realization of $S_n$ deviate from the
almost sure behavior. These results apply to the fluctuations of Brownian
motion, Birkhoff averages on hyperbolic dynamics, as well as branching random
walks. Also, they lead to new insights into the "randomness" of the digits of
expansions in integer bases of Pi. We formulate a new conjecture, supported by
numerical experiments, implying the normality of Pi.

6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas