Convergence from wave to particle

It seems that the process of the changing from wave to particle may be a process of convergence, in which the convergence speed of wave or bottom layer/field is much higher than the logic speed/light speed of discrete presentation layer in this universe to ensure that a somehow discrete result can be got in time, and in which the least action principal ensure that this process is convergence (stable? reliable? with achievable result?), and after convergence there should be a divergence process as well in which a certainized discrete particle becomes uncertain waves again.