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The expected number of distinct sites visited by N biased random walks in one dimension

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  • Larralde, Hernan
  • Weiss, George H.
  • Eugene Stanley, H.

Abstract

We calculate the asymptotic form of the expected number of distinct sites visited by N random walkers moving independently in one dimension. It is shown that to lowest order and at long times, the leading term in the asymptotic result is that found for the random walk of a single biased particle, which implies that the bias is strong enough a factor to dominate the many-body effects in that regime. The lowest order correction term contains the many-body contribution. This is essentially the result for the unbiased random walk.

Suggested Citation

  • Larralde, Hernan & Weiss, George H. & Eugene Stanley, H., 1994. "The expected number of distinct sites visited by N biased random walks in one dimension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 209(3), pages 361-368.
    • Handle: RePEc:eee:phsmap:v:209:y:1994:i:3:p:361-368
    DOI: 10.1016/0378-4371(94)90189-9
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