Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Branching random walk in random environment with random absorption wall   We consider the branching random walk in random environment with a random
absorption wall. When we add this barrier, we discuss some topics related to
the survival probability. We assume that the random environment is i.i.d.,
$S_i$ is a particular i.i.d. random walk depend on the random environment
$\mathcal{L}$. Let the random barrier function (the random absorption wall) is
$g_i(\mathcal{L}):=ai^\alpha-S_i,$ where $i$ present the generation. We show
that there exists a critical value $a_c>0$ such that if
$a>a_c,\alpha=\frac{1}{3}$, the survival probability is positive almost surly
and if $a<a_c,\alpha=\frac{1}{3}$ ,the survival probability is zero almost
surely. Moreover, if we denote $Z_n$ is the total populations in $n$-th
generation in the new system (with barrier),under some conditions, we show
$\ln\mathbb{P}_{\mathcal{L}}(Z_n>0)/n^{1/3}$ will converges to a negative
constant almost surely if $\alpha\in[0,\frac{1}{3})$.

33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin