Extreme value statistics of positive recurrent centrally biased random walks. (1st October 2022) - Artuso, Roberto; Onofri, Manuele; Pozzoli, Gaia; Radice, Mattia
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.