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Synchronization of random walks with reflecting boundaries
Citation key Ruttor:2004:SRW
Author Andreas Ruttor and Georg Reents and Wolfgang Kinzel
Pages 8609-8618
Year 2004
DOI 10.1088/0305-4470/37/36/003
Journal J. Phys. A: Math. Gen.
Volume 37
Abstract 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 analysed, which converges to a geometric distribution for long synchronization times. From this asymptotic behaviour 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.
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