Collision statistics for random flights with anisotropic scattering and absorption

Abstract

For a broad class of random walks with anisotropic scattering kernel and absorption, we derive explicit formulas that allow expressing the moments of the collision number $n_V$ performed in a volume $V$ as a function of the particle equilibrium distribution. Our results apply to arbitrary domains $V$ and boundary conditions, and allow assessing the hitting statistics for systems where the typical displacements are comparable to the domain size, so that the diffusion limit is possibly not attained. An example is discussed for one-dimensional (1d) random flights with exponential displacements, where analytical calculations can be carried out.

9 pages, 5 figures

References in corpus (7)

• First-passage times in complex scale-invariant media
• On distributions of functionals of anomalous diffusion paths
• Mean first-passage time of surface-mediated diffusion in spherical domains
• Asymptotic behavior of self-affine processes in semi-infinite domains
• Collision densities and mean residence times for $d$-dimensional exponential flights
• Collision number statistics for transport processes
• Residence time and collision statistics for exponential flights: the rod problem revisited

Cited by in corpus (7)

• Properties of branching exponential flights in bounded domains
• Branching exponential flights: travelled lengths and collision statistics
• Cauchy's formulas for random walks in bounded domains
• Strongly constrained stochastic processes: the multi-ends Brownian bridge
• Counting statistics: a Feynman-Kac perspective
• Discrete Feynman-Kac formulas for branching random walks
• Surprising variants of Cauchy's formula for mean chord length