On the distribution of random integer-valued quantities obeying to some arithmetical inequality

In V.P. Maslov's works, the problems of cumulative probabilities of distribution of the system of many identical particles to the energy levels for different conditions to the number of particles, the total energy and dimension of the system are studied from the mathematical point of view. It is supposed that all possibilities that obey to the same conditions, are equiprobable.
In the talk, we consider a problem of distribution of identical particles in the system with several centers. The total energy is set to be equal to the product of total energies corresponding to different centers. We find the asymptotic cumulative distribution and the entropy for the system under considering.