  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.
