  We address the question of the relevance of thermalization to the increase of
correlations in the quench dynamics of an isolated system with a finite number
of interacting bosons. Specifically, we study how, in the process of
thermalization, the correlations between occupation numbers increase in time
resulting in the emergence of the Bose-Einstein distribution. We show, both
analytically and numerically, that before saturation the two-point correlation
function increases quadratically in time. This time dependence is at variance
with the exponential increase of the number of principal components of the wave
function, recently discovered and explained in Ref.\cite{BIS18}. We also
demonstrate that the out-of-time-order correlator (OTOC) increases
algebraically in time but not exponentially as predicted in many publications.
Our results, that can be confirmed experimentally in traps with interacting
bosons, may be also relevant to the problem of black hole scrambling.
