Extreme value statistics of positive recurrent centrally biased random walks

Abstract

We consider the extreme value statistics of centrally-biased random walks with asymptotically-zero drift in the ergodic regime. We fully characterize the asymptotic distribution of the maximum for this class of Markov chains lacking translational invariance, with a particular emphasis on the relation between the time scaling of the expected value of the maximum and the stationary distribution of the process.

26 pages, 6 figures

References in corpus (4)

• Universal Record Statistics of Random Walks and Lévy Flights
• Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap
• Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit
• Excursions and path functionals for stochastic processes with asymptotically zero drifts