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Conference in memory of A. A. Karatsuba on number theory and applications, 2015
January 31, 2015 15:30–15:55, Moscow, Steklov Mathematical Institute of the Russian Academy of Sciences
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On the distribution of random integer-valued quantities obeying to some arithmetical
inequality
G. V. Fedorovab
a Institute for System Research, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract:
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.
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