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


  • Satya N. Majumdar
  • Philippe Mounaix
  • Gregory Schehr


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

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  • Satya N. Majumdar & Philippe Mounaix & Gregory Schehr, 2013. "Exact Statistics of the Gap and Time Interval Between the First Two Maxima of Random Walks," Papers 1303.4607,
  • Handle: RePEc:arx:papers:1303.4607

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    1. repec:eee:phsmap:v:485:y:2017:i:c:p:48-60 is not listed on IDEAS
    2. Claude Godreche & Satya N. Majumdar & Gregory Schehr, 2017. "Record statistics of a strongly correlated time series: random walks and L\'evy flights," Papers 1702.00586,

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