Exact Statistics of the Gap and Time Interval Between the First Two Maxima of Random Walks

Satya N. Majumdar, Philippe Mounaix and Gregory Schehr
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Satya N. Majumdar: LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques - UP11 - Université Paris-Sud - Paris 11 - CNRS - Centre National de la Recherche Scientifique
Philippe Mounaix: CPHT - Centre de Physique Théorique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Gregory Schehr: LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques - UP11 - Université Paris-Sud - Paris 11 - CNRS - Centre National de la Recherche Scientifique

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Abstract: We investigate the statistics of the gap, G_n, between the two rightmost positions of a Markovian one-dimensional random walker (RW) after n time steps and of the duration, L_n, which separates the occurrence of these two extremal positions. The distribution of the jumps \eta_i's of the RW, f(\eta), is symmetric and its Fourier transform has the small k behavior 1-\hat{f}(k)\sim| k|^\mu with 0

Date: 2013
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Citations: View citations in EconPapers (4)

Published in Physical Review Letters, 2013, 111, pp.070601

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00861416

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