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.

arXiv comment5 pages, 2 figures

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Cited by in corpus (6)

• Monte Carlo particle transport in random media: the effects of mixing statistics
• Cauchy's formulas for random walks in bounded domains
• Clustering of branching Brownian motions in confined geometries
• Invariance property in inhomogeneous scattering media with refractive-index mismatch
• Universal properties of branching random walks in confined geometries
• A universal property of random trajectories in bounded domains