  Periodic orbits in chaotic systems form clusters, whose elements traverse
approximately the same points of the phase space. The distribution of cluster
sizes depends on the length n of orbits and the parameter p which controls
closeness of orbits actions. We show that counting of cluster sizes in the
baker's map can be turned into a spectral problem for an ensemble of truncated
unitary matrices. Based on the conjecture of the universality for the
eigenvalues distribution at the spectral edge of these ensembles, we obtain
asymptotics of the second moment of cluster distribution in a regime where both
n and p tend to infinity. This result allows us to estimate the average cluster
size as a function of the number of encounters in periodic orbits.
