Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Branching Brownian Motion Conditioned on Particle Numbers   We study analytically the order and gap statistics of particles at time $t$
for the one dimensional branching Brownian motion, conditioned to have a fixed
number of particles at $t$. The dynamics of the process proceeds in continuous
time where at each time step, every particle in the system either diffuses
(with diffusion constant $D$), dies (with rate $d$) or splits into two
independent particles (with rate $b$). We derive exact results for the
probability distribution function of $g_k(t) = x_k(t) - x_{k+1}(t)$, the
distance between successive particles, conditioned on the event that there are
exactly $n$ particles in the system at a given time $t$. We show that at large
times these conditional distributions become stationary $P(g_k, t \to \infty|n)
= p(g_k|n)$. We show that they are characterised by an exponential tail
$p(g_k|n) \sim \exp[-\sqrt{\frac{|b - d|}{2 D}} ~g_k]$ for large gaps in the
subcritical ($b < d$) and supercritical ($b > d$) phases, and a power law tail
$p(g_k) \sim 8\left(\frac{D}{b}\right){g_k}^{-3}$ at the critical point ($b =
d$), independently of $n$ and $k$. Some of these results for the critical case
were announced in a recent letter [K. Ramola, S. N. Majumdar and G. Schehr,
Phys. Rev. Lett. 112, 210602 (2014)].

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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph