Motion in bounded domains represents a paradigm in several settings: from billiard dynamics, to random walks in a finite lattice, with applications to relevant physical, ecological, and biological problems. A remarkable universal property, involving the average of return times to the boundary, has been theoretically proposed and experimentally verified in quite different contexts. We discuss here mechanisms that lead to violations of universality, induced by boundary effects and we also emphasize the role played by replacing straight lines with random walks in this framework. We suggest that our analysis should be relevant where nonhomogeneity appears in the stationary probability distribution in bounded domain.
Cauchy universality and random billiards
Artuso R.Primo
;Zamora D. J.Secondo
2024-01-01
Abstract
Motion in bounded domains represents a paradigm in several settings: from billiard dynamics, to random walks in a finite lattice, with applications to relevant physical, ecological, and biological problems. A remarkable universal property, involving the average of return times to the boundary, has been theoretically proposed and experimentally verified in quite different contexts. We discuss here mechanisms that lead to violations of universality, induced by boundary effects and we also emphasize the role played by replacing straight lines with random walks in this framework. We suggest that our analysis should be relevant where nonhomogeneity appears in the stationary probability distribution in bounded domain.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.