Synchronization of random walks with reflecting boundaries

Details Synchronization of random walks with reflecting boundaries Synchronization of random walks with reflecting boundaries

2004-05-17

arxiv.org/abs/cond-mat/0405369v2

J. Phys. A: Math. Gen. 37 (2004) 8609-8618

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, 7 figures; introduction changed, typos corrected

Scientific paper

10.1088/0305-4470/37/36/003

Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are found to increase proportional to the square of the system size. Additionally, the probability of synchronization in a given step is analyzed, which converges to a geometric distribution for long synchronization times. From this asymptotic behavior the number of steps required to synchronize an ensemble of independent random walk pairs is deduced. Here the synchronization time increases with the logarithm of the ensemble size. The results of this model are compared to those observed in neural synchronization.

Affiliated with

Also associated with

No associations

Rating

Synchronization of random walks with reflecting boundaries 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 Synchronization of random walks with reflecting boundaries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Synchronization of random walks with reflecting boundaries will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-284673