Spherically symmetric random walks in noninteger dimension
- Department of Physics, Washington University, St. Louis, Missouri 63130-4899 (United States)
- Department of Physics, Brookhaven National Laboratory, Upton, New York 11973 (United States)
- Department of Physics, Technion Israel Institute of Technology, Haifa 32000 (Israel)
A previous article proposed a new kind of random walk on a spherically symmetric lattice in arbitrary noninteger dimension [ital D]. Such a lattice avoids the problems associated with a hypercubic lattice in noninteger dimension. This article examines the nature of spherically symmetric random walks in detail. A large-time asymptotic analysis of these random walks is performed and the results are used to determine the Hausdorff dimension of the process. Exact results are obtained in terms of Hurwitz functions (incomplete zeta functions) for the probability of a walker going from one region of the spherical lattice to another. Finally, it is shown that the probability that the paths of [ital K] independent random walkers will intersect vanishes in the continuum limit if [ital D][gt]2[ital K]/([ital K][minus]1).
- OSTI ID:
- 7253328
- Journal Information:
- Journal of Mathematical Physics (New York); (United States), Vol. 35:9; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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