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26 April 2024
 
  » pubmed » pmid12241402

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Number of distinct sites visited by a random walker trapped by an absorbing boundary
Leonardo Dagdug ; Alexander M Berezhkovskii ; George H Weiss ;
Date 30 Jun 2002
Journal Phys Rev E, 66 (1 Pt 1), 012901
AbstractThe number of distinct sites visited by a lattice random walker is a subject of continuing interest in both mathematics and physics. All previous investigations have used the assumption that the lattice is unbounded. An assessment of the amount of tissue interrogated by a photon in reflectance measurements for diagnostic purposes suggests analyzing properties of the average number of distinct sites visited by a random walker trapped by an absorbing plane at time t. We show that for sufficiently large t this number is the same as the average number of distinct sites visited for this time when the surface is not present. A more complete analysis is possible for a random walk on a line terminated by an absorbing point.
Source PubMed, pmid12241402
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