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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 | Abstract: | The 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 | Services: | Forum | Review | Favorites |
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