Some Problems from the Bernoulli Symbolic Dynamics

Student: Israfilova Ainur

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2020

The present paper contains introduction and two sections. In the first part we prove the limit theorems for the first collision time and for the number of the boxes containing more than one particle in the Maxwell–Boltzmann (MB) scheme. These results are well known, but we use elementary combinatorial methods applicable in the more general situations (non-symmetric MB(N,n) schemes, dependent boxes etc.) In the second part we study the similar problems for the generalized Kalman - Singer Markov chains. We consider two kind of generalization: the arbitrary value of the shift of the window and the general distribution of the letters in the finite alphabet. In some cases we have Poisson limit theorem (like in MB(N,n) model), in other we have compound Poisson distribution.

Full text (added June 1, 2020)

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