Territory covered by N random walkers

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 4, 1999, Pages

  Yuste, S B ^a   Acedo, L ^a  

^a UNIVERSITY OF EXTREMADURA   (Spain)

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[No Author keywords available]

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ARTICLE;

EID: 0001260975     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.R3459     Document Type: Article

References (32)

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16. This statement should be changed if one interprets that for (Formula presented) and (Formula presented) the expressions obtained in 6 give implicitly a first-order corrective term. In this case, this term only partially gives the first-order correction to the main term and should be complemented with other first-order corrective terms [see the discussion following Eq. (12)].
17. The paper by G.M. Sastry and N. Agmon [J. Chem. Phys. 104, 3022 (1996)] is, for the one-dimensional case, an exception to this statement, and the value given there for (Formula presented) is correct. However, their method uses some uncontrolled approximations and it is not possible to know a priori whether the expressions obtained are fully correct. For example, their corrective terms are not the rigorously derived ones.
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27. Let (Formula presented) be the probability that in the time interval (Formula presented) a single diffusing particle that starts at a site is not trapped by an absorbing frontier placed at distance r. For some kinds of fractal 18 this probability has the functional form given in Eq. (4). Besides, it can be argued that (Formula presented) and (Formula presented) are approximately proportional to each other for large (Formula presented), so that Eq. (4) is also valid for that class of fractals.
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29. We attribute this discrepancy to the fact that Larralde et al. approximate (Formula presented) by (Formula presented) for small x [see, for example, Eq. (3.10) of Ref. 7]. The correct value is (Formula presented).
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32. See Fig. 3 of 6, or the figure of 4, or cover of 3.