Counting statistics a Feynman-Kac perspective

A. Zoia (1) , E. Dumonteil (1) , A. Mazzolo (1)

1 CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire)

By building upon a Feynman-Kac formalism, we assess the distribution of the number of collisions in a given region for a broad class of discrete-time random walks in absorbing and non absorbing media. We derive the evolution equation for the generating function of the number of collisions, and complete our analysis by examining the moments of the distribution, and their relation to the walker equilibrium density. Some significant applications are discussed in detail in particular, we revisit the gambler-s ruin problem and generalize to random walks with absorption the arcsine law for the number of collisions on the half-line.

Keywords: collisions; statistique; Monte Carlo

Domains: Physics [physics]; Nuclear Experiment [nucl-ex]; Physics [physics]; Nuclear Theory [nucl-th]

A. Zoia, E. Dumonteil, A. Mazzolo. Counting statistics a Feynman-Kac perspective. Physical Review E , 2012, 85, pp.011132. ⟨10.1103/PhysRevE.85.011132⟩. ⟨cea-02349241⟩