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On the range of a constrained random walk

Published online by Cambridge University Press:  14 July 2016

W. Th. F. Den Hollander  and
G. H. Weiss
W. Th. F. Den Hollander*
Affiliation:
Delft University of Technology
G. H. Weiss*
Affiliation:
National Institutes of Health
*
∗ Postal address: Department of Mathematics, Delft University of Technology, Julianalaan 132, 2628 BL Delft, The Netherlands.
∗∗ Postal address: Division of Computer Research and Technology, National Institutes of Health, Bethesda, MD 20892, USA.
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Abstract

We study statistical properties of the range (= number of distinct sites visited) of a lattice random walk in discrete time constrained to visit a given site at a given time. In particular, we calculate the mean and obtain a bound on the variance of the range in the large time limit. The results are applied to a problem involving an unconstrained random walk in the presence of randomly distributed traps. A key role is played by the associated random walk that is obtained from the original random walk via a Cramer transform.

Keywords

RATIO LIMIT THEOREMTRAPPING
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 451 - 463
Copyright
Copyright © Applied Probability Trust 1988 

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