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

Satya N. Majumdar, Philippe Mounaix and Gregory Schehr

Papers from arXiv.org

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: 2013-03
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Published in Phys. Rev. Lett. 111, 070601 (2013)

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