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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On infinite connected real networks without cycles
\, their dynamical systems and pseudorandom and ra
ndom real sequences - Vasyl Ustimenko (Maria Curie
-Sklodowska University\, National Academy of Scien
ces of Ukraine\, National University of Kyiv)
DTSTART;TZID=Europe/London:20220325T110000
DTEND;TZID=Europe/London:20220325T113000
UID:TALK171731AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/171731
DESCRIPTION:The family of graphs $I_n$ will be introduced as a
pproximation of network $T$ . It means that they a
re bipartite grahs with the set of points and line
s isomorphic to $[0\,1)^n$\, $n>1$ such rhat their
projective limit is well defined and coincides wi
th $I.$ We prove that $I_n$ is a family of small w
orld graphs of large girth. It means that the girt
h and diamrter of $I_n$ are linear expressions in
variable $n$\nWe consider application of $I$ to se
cure transition of nondeterministic real strings o
f pseudorandom sequences of numbers of interval $[
0\,1)$.Graph $I$ satisfies to the definition of ti
me-like graph [1]. So path in the graph can be an
instrument for the time measurement of corresponde
nt Markovian process.\nReferences\,\n[1] .K. Burdy
\, S.Pal\, Markov processes on time like graphs\,T
he Annals of Probability\,2011\, Vol. 39\, No. 4\,
1332&ndash\;1364\nDOI: 10.1214/10-AOP583
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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