Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random trees and applications   We discuss several connections between discrete and continuous random trees.
In the discrete setting, we focus on Galton-Watson trees under various
conditionings. In particular, we present a simple approach to Aldous' theorem
giving the convergence in distribution of the contour process of conditioned
Galton-Watson trees towards the normalized Brownian excursion. We also briefly
discuss applications to combinatorial trees. In the continuous setting, we use
the formalism of real trees, which yields an elegant formulation of the
convergence of rescaled discrete trees towards continuous objects. We explain
the coding of real trees by functions, which is a continuous version of the
well-known coding of discrete trees by Dyck paths. We pay special attention to
random real trees coded by Brownian excursions, and in a particular we provide
a simple derivation of the marginal distributions of the CRT. The last section
is an introduction to the theory of the Brownian snake, which combines the
genealogical structure of random real trees with independent spatial motions.
We introduce exit measures for the Brownian snake and we present some
applications to a class of semilinear partial differential equations.

32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con