Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On large deviation probabilities for empirical distribution of branching
  random walks: Schr{\"o}der case and B{\"o}ttcher case   Given a super-critical branching random walk on $\mathbb{R}$ started from the
origin, let $Z\_n(\cdot)$ be the counting measure which counts the number of
individuals at the $n$-th generation located in a given set. Under some mild
conditions, it is known in \cite{B90} that for any interval $A\subset
\mathbb{R}$, $\frac{Z\_n(\sqrt{n}A)}{Z\_n(\mathbb{R})}$ converges a.s. to
$\nu(A)$, where $\nu$ is the standard Gaussian measure. In this work, we
investigate the convergence rates of
$$\mathbb{P}\left(\frac{Z\_n(\sqrt{n}A)}{Z\_n(\mathbb{R})}-\nu(A)>\Delta\right),$$
for $\Delta\in (0, 1-\nu(A))$, in both Schr{\"o}der case and B{\"o}ttcher case.

30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys