Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monte Carlo study of the tip region of branching random walks evolved to
  large times   We implement a discretization of the one-dimensional branching Brownian
motion in the form of a Monte Carlo event generator, designed to efficiently
produce ensembles of realizations in which the rightmost lead particle at the
final time $T$ is constrained to have a position $X$ larger than some
predefined value $X_{\text{min}}$. The latter may be chosen arbitrarily far
from the expectation value of $X$, and the evolution time after which
observables on the particle density near the lead particle are measured may be
as large as $T\sim 10^4$. We then calculate numerically the probability
distribution $p_n(\Delta x)$ of the number $n$ of particles in the interval
$[X-\Delta x,X]$ as a function of $\Delta x$. When $X_{\text{min}}$ is
significantly smaller than the expectation value of the position of the
rightmost lead particle, i.e. when $X$ is effectively unconstrained, we check
that both the mean and the typical values of $n$ grow exponentially with
$\Delta x$, up to a linear prefactor and to finite-$T$ corrections. When
$X_{\text{min}}$ is picked far ahead of the latter but within a region
extending over a size of order $\sqrt{T}$ to its right, the mean value of the
particle number still grows exponentially with $\Delta x$, but its typical
value is lower by a multiplicative factor consistent with $e^{-\zeta\Delta
x^{2/3}}$, where $\zeta$ is a number of order unity. These numerical results
bring strong support to recent analytical calculations and conjectures in the
infinite-time limit.

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The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg