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Probabilistic picture for particle number densities in stretched tips of the branching Brownian motion

Journal Article · · Europhysics Letters
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Abstract

In the framework of a stochastic picture for the one-dimensional branching Brownian motion, we compute the probability density of the number of particles near the rightmost one at a timeT, that we take very large, when this extreme particle is conditioned to arrive at a predefined positionxTchosen far ahead of its expected positionmT. We recover the previously conjectured fact that the typical number density of particles at a distance Δ to the left of the lead particle, when both Δ andare large, is smaller than the mean number density by a factor proportional to, whereζis a constant that was so far undetermined. Our picture leads to an expression for the probability density of the particle number, from which a value forζmay be inferred.

Research Organization:
Columbia Univ., New York, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
FG02-92ER40699
OSTI ID:
2419386
Journal Information:
Europhysics Letters, Journal Name: Europhysics Letters Journal Issue: 5 Vol. 140; ISSN 0295-5075
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English

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Physics