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arXiv · 2207.07367

Extreme value statistics of positive recurrent centrally biased random walks

Roberto Artuso·Manuele Onofri·Gaia Pozzoli·Mattia Radice
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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.

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Roberto Artuso, Manuele Onofri, Gaia Pozzoli, Mattia Radice. 2022-07-15. Extreme value statistics of positive recurrent centrally biased random walks. https://doi.org/10.1088/1742-5468%2Fac98bd

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