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.

arXiv comment26 pages, 6 figures

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• Records and occupation time statistics for area-preserving maps