Number of distinct sites visited by N random walkers on a Euclidean lattice

Дата и время публикации : 2000-02-23T17:16:28Z

Авторы публикации и институты :
S. B. Yuste
L. Acedo

Ссылка на журнал-издание: Phys. Rev. E, vol. 61, n. 3, 2340-2347 (2000)
Коментарии к cтатье: 15 pages (RevTex), 4 figures (eps); to appear in Phys. Rev. E
Первичная категория: cond-mat.stat-mech

Все категории : cond-mat.stat-mech, cond-mat.dis-nn

Краткий обзор статьи: The evaluation of the average number S_N(t) of distinct sites visited up to time t by N independent random walkers all starting from the same origin on an Euclidean lattice is addressed. We find that, for the nontrivial time regime and for large N, S_N(t) approx hat S_N(t) (1-Delta), where hat S_N(t) is the volume of a hypersphere of radius (4Dt ln N)^{1/2}, Delta={1/2}sum_{n=1}^infty ln^{-n} N sum_{m=0}^n s_m^{(n)} ln^{m} ln N, d is the dimension of the lattice, and the coefficients s_m^{(n)} depend on the dimension and time. The first three terms of these series are calculated explicitly and the resulting expressions are compared with other approximations and with simulation results for dimensions 1, 2, and 3. Some implications of these results on the geometry of the set of visited sites are discussed.

Category: Physics