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Record Statistics for Multiple Random Walks

Listed author(s):
  • Gregor Wergen
  • Satya N. Majumdar
  • Gregory Schehr
Registered author(s):

    We study the statistics of the number of records R_{n,N} for N identical and independent symmetric discrete-time random walks of n steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. We consider two cases: (I) when the variance \sigma^2 of the jump distribution is finite and (II) when \sigma^2 is divergent as in the case of L\'evy flights with index 0 grows universally as \sim \alpha_N \sqrt{n} for large n, but with a very different behavior of the amplitude \alpha_N for N > 1 in the two cases. We find that for large N, \alpha_N \approx 2 \sqrt{\log N} independently of \sigma^2 in case I. In contrast, in case II, the amplitude approaches to an N-independent constant for large N, \alpha_N \approx 4/\sqrt{\pi}, independently of 0

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    Paper provided by in its series Papers with number 1204.5039.

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    Date of creation: Apr 2012
    Publication status: Published in Phys. Rev. E 86, 011119 (2012)
    Handle: RePEc:arx:papers:1204.5039
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