Sisyphus random walk

21 Jul 2016  ·  Montero Miquel, Villarroel Javier ·

In this paper we consider a particular version of the random walk with restarts: random reset events which bring suddenly 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 associated naturally to the system. Finally we indicate feasible generalizations useful for interpreting different physical effects. read more

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Mathematical Physics Statistical Mechanics Mathematical Physics Probability