Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalized model interpolating between the random energy model and
  the branching random walk   We study a generalization of the model introduced by Kistler and Schmidt in
$2015$, that interpolates between the random energy model (REM) and the
branching random walk (BRW). More precisely, we are interested in the
asymptotic behaviour of the extremal process associated to this model. Kistler
and Schmidt show that the extremal process of the $GREM(N^{\alpha})$,
$\alpha\in{[0,1)}$ converges weakly to a simple Poisson point process. This
contrasts with the extremal process of the branching random walk $(\alpha=1)$
which was shown to converge toward a decorate Poisson point process by Madaule.
In this paper we propose a generalized model of the $GREM(N^{\alpha})$, that
has the structure of a tree with $k_n$ levels, where $(k_n\leq n)$ is a
non-decreasing sequence of positive integers. We study a generalized case,
where the position of the particles are not necessarily Gaussian variables and
the reproduction law is not necessarily binary. We show that as long as
$b_n=\lfloor{\frac{n}{k_n}}\rfloor\to_{n\to \infty}\infty$ in the Gaussian case
(with the assumption $\frac{b_n}{\log(n)^2}\to\infty$ as $n\to \infty$ in the
non Gaussian case) the decoration disappears and we have convergence to a
simple Poisson point process.

30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph