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We consider the extreme value statistics of centrally-biased random walkswith asymptotically-zero drift in the ergodic regime. We fully characterize theasymptotic distribution of the maximum for this class of Markov chains lackingtranslational invariance, with a particular emphasis on the relation betweenthe time scaling of the expected value of the maximum and the stationarydistribution of the process.

Extreme value statistics of positive recurrent centrally biased random walks