Hernán Larralde and George H Weiss 2003 J. Phys. A: Math. Gen. 36 8367 doi:10.1088/0305-4470/36/31/302
Hernán Larralde1 and George H Weiss2
Show affiliationsIn earlier work we have studied the expected number of distinct sites (ENDS) visited by N random walkers in time t on a translationally invariant lattice. Optical applications suggest the interest in analysing the same problem for a semi-infinite lattice in three dimensions bounded by a plane of absorbing sites. We here study this problem, showing a multiplicity of time regimes, and at the longest times showing that the ENDS is proportional to N√t where t is the time. In the absence of a boundary the comparable result is proportional to Nt. Thus, the boundary effect eliminates approximately √t random walks.
Issue 31 (8 August 2003)
Received 23 April 2003
Published 23 July 2003
Hernán Larralde and George H Weiss 2003 J. Phys. A: Math. Gen. 36 8367
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