Downsizing from the merging model point of view (preliminary discussion

In the four-particle scattering processes with mass transfer, unlike mergers in which mass can only increase, an essential role are played the processes, when the mass of the most massive galaxies can be decreased. Elementary model describing such a process is considered. In this respect, it is supposed to explain the observed phenomenon of ''downsizing'' when with cosmological time the growth of characteristic mass of the heaviest galaxies is followed by its decrease