Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random walks on hyperbolic spaces: second order expansion of the rate
  function at the drift   Let $(X,d)$ be a geodesic Gromov-hyperbolic space, $o \in X$ a basepoint and
$\mu$ a countably supported non-elementary probability measure on
$\operatorname{Isom}(X)$. Denote by $z_n$ the random walk on $X$ driven by the
probability measure $\mu$. Supposing that $\mu$ has finite exponential moment,
we give a second-order Taylor expansion of the large deviation rate function of
the sequence $\frac{1}{n}d(z_n,o)$ and show that the corresponding coefficient
is expressed by the variance in the central limit theorem satisfied by the
sequence $d(z_n,o)$. This provides a positive answer to a question raised in
\cite{BMSS}. The proof relies on the study of the Laplace transform of
$d(z_n,o)$ at the origin using a martingale decomposition first introduced by
Benoist--Quint together with an exponential submartingale transform and large
deviation estimates for the quadratic variation process of certain martingales.

3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an