title: Directed random walk with random restarts: The Sisyphus random walk.
abstract: In this paper we consider a particular version of the random walk with restarts: random reset events which suddenly bring the system to the starting value. We analyze its relevant statistical properties, like the transition probability, and show how an equilibrium state appears. Formulas for the first-passage time, high-water marks, and other extreme statistics are also derived; we consider counting problems naturally associated with the system. Finally we indicate feasible generalizations useful for interpreting different physical effects.
authors.affiliation: Secció de Física Estadística i Interdisciplinària, Departament de Física de la Matèria Condensada, Universitat de Barcelona (UB), Martí i Franquès 1, E-08028 Barcelona, Spain and Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona, Spain.
authors.forename: Miquel
authors.initials: M
authors.lastname: Montero
authors.affiliation: Facultad de Ciencias & Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca, Plaza Merced s/n, E-37008 Salamanca, Spain.
authors.forename: Javier
authors.initials: J
authors.lastname: Villarroel