Residence time and collision statistics for exponential flights: the rod problem revisited

Abstract

Many random transport phenomena, such as radiation propagation, chemical/biological species migration, or electron motion, can be described in terms of particles performing {\em exponential flights}. For such processes, we sketch a general approach (based on the Feynman-Kac formalism) that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution. We then illustrate the proposed method in the case of the so-called {\em rod problem} (a 1d system), and discuss the relevance of the obtained results in the context of Monte Carlo estimators.

9 pages, 8 figures

References in corpus (4)

• First-passage times in complex scale-invariant media
• Collision densities and mean residence times for $d$-dimensional exponential flights
• A new family of solvable Pearson-Dirichlet random walks
• Collision number statistics for transport processes

Cited by in corpus (4)

• Branching exponential flights: travelled lengths and collision statistics
• Cauchy's formulas for random walks in bounded domains
• Counting statistics: a Feynman-Kac perspective
• Collision statistics for random flights with anisotropic scattering and absorption