On infinite connected real networks without cycles, their dynamical systems and pseudorandom and random real sequences

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• Vasyl Ustimenko (Maria Curie-Sklodowska University, National Academy of Sciences of Ukraine, National University of Kyiv)
• Friday 25 March 2022, 11:00-11:30
• Seminar Room 1, Newton Institute.

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FD2W02 - Fractional kinetics, hydrodynamic limits and fractals

The family of graphs $I_n$ will be introduced as approximation of network $T$ . It means that they are bipartite grahs with the set of points and lines isomorphic to $[0,1)^n$, $n>1$ such rhat their projective limit is well defined and coincides with $I.$ We prove that $I_n$ is a family of small world graphs of large girth. It means that the girth and diamrter of $I_n$ are linear expressions in variable $n$ We consider application of $I$ to secure transition of nondeterministic real strings of pseudorandom sequences of numbers of interval $[0,1)$.Graph $I$ satisfies to the definition of time-like graph [1]. So path in the graph can be an instrument for the time measurement of correspondent Markovian process. References, [1] .K. Burdy, S.Pal, Markov processes on time like graphs,The Annals of Probability,2011, Vol. 39, No. 4, 1332–1364 DOI : 10.1214/10-AOP583

This talk is part of the Isaac Newton Institute Seminar Series series.

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