title: 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 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 rod problem (a one-dimensional system), and discuss the relevance of the obtained results in the context of Monte Carlo estimators.
authors.affiliation: CEA/Saclay, DEN/DANS/DM2S/SERMA/LTSD, F-91191 Gif-sur-Yvette, France. andrea.zoia@cea.fr
authors.forename: A
authors.initials: A
authors.lastname: Zoia
authors.forename: E
authors.initials: E
authors.lastname: Dumonteil
authors.forename: A
authors.initials: A
authors.lastname: Mazzolo