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

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

2000-02-23

arxiv.org/abs/cond-mat/0002362v1

Phys. Rev. E, vol. 61, n. 3, 2340-2347 (2000)

Physics

Condensed Matter

Statistical Mechanics

15 pages (RevTex), 4 figures (eps); to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.61.2340

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.

Affiliated with

Also associated with

No associations

Rating

Number of distinct sites visited by N random walkers on a Euclidean lattice does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Number of distinct sites visited by N random walkers on a Euclidean lattice, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Number of distinct sites visited by N random walkers on a Euclidean lattice will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-506710