Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transition, scaling of moments, and order-parameter distributions
  in Brownian particles and branching processes with finite-size effects   We revisit the problem of Brownian diffusion with drift in order to study
finite-size effects in the geometric Galton-Watson branching process. This is
possible because of an exact mapping between one-dimensional random walks and
geometric branching processes, known as the Harris walk. In this way,
first-passage times of Brownian particles are equivalent to sizes of trees in
the branching process (up to a factor of proportionality). Brownian particles
that reach a distant boundary correspond to percolating trees, and those that
do not correspond to non-percolating trees. In fact, both systems display a
second-order phase transition between "insulating" and "conducting" phases,
controlled by the drift velocity in the Brownian system. In the limit of large
system size, we obtain exact expressions for the Laplace transforms of the
probability distributions and their first and second moments. These quantities
are also shown to obey finite-size scaling laws.

8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc