University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > On infinite connected real networks without cycles, their dynamical systems and pseudorandom and random real sequences

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

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  • UserVasyl Ustimenko (Maria Curie-Sklodowska University, National Academy of Sciences of Ukraine, National University of Kyiv)
  • ClockFriday 25 March 2022, 11:00-11:30
  • HouseSeminar 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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