Properties of branching exponential flights in bounded domains

Abstract

Branching random flights are key to describing the evolution of many physical and biological systems, ranging from neutron multiplication to gene mutations. When their paths evolve in bounded regions, we establish a relation between the properties of trajectories starting on the boundary and those starting inside the domain. Within this context, we show that the total length travelled by the walker and the number of performed collisions in bounded volumes can be assessed by resorting to the Feynman-Kac formalism. Other physical observables related to the branching trajectories, such as the survival and escape probability, are derived as well.

5 pages, 2 figures

References in corpus (6)

• First-passage times in complex scale-invariant media
• Fractional Laplacian in Bounded Domains
• The survival probability of a branching random walk in presence of an absorbing wall
• Branching exponential flights: travelled lengths and collision statistics
• Collision number statistics for transport processes
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Cited by in corpus (3)

• Cauchy's formulas for random walks in bounded domains
• Clustering of branching Brownian motions in confined geometries
• Universal properties of branching random walks in confined geometries