Counting statistics: a Feynman-Kac perspective

Details Counting statistics: a Feynman-Kac perspective Counting statistics: a Feynman-Kac perspective

2011-12-14

arxiv.org/abs/1112.3368v1

Phys. Rev. E 85, 011132 (2012)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 6 figures

Scientific paper

10.1103/PhysRevE.85.011132

By building upon a Feynman-Kac formalism, we assess the distribution of the number of hits in a given region for a broad class of discrete-time random walks with scattering and absorption. We derive the evolution equation for the generating function of the number of hits, 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 hits on the half-line.

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