BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:On infinite connected real networks without cycles\, their dynamic
 al systems and pseudorandom and random real sequences - Vasyl Ustimenko (M
 aria Curie-Sklodowska University\, National Academy of Sciences of Ukraine
 \, National University of Kyiv)
DTSTART:20220325T110000Z
DTEND:20220325T113000Z
UID:TALK171731@talks.cam.ac.uk
DESCRIPTION: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 p
 oints and lines isomorphic to $[0\,1)^n$\, $n>1$ such rhat their projectiv
 e limit is well defined and coincides with $I.$ We prove that $I_n$ is a f
 amily of small world graphs of large girth. It means that the girth and di
 amrter of $I_n$ are linear expressions in variable $n$\nWe consider applic
 ation of $I$ to secure transition of nondeterministic real strings of pseu
 dorandom 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 inst
 rument for the time measurement of correspondent Markovian process.\nRefer
 ences\,\n[1] .K. Burdy\, S.Pal\, Markov processes on time like graphs\,The
  Annals of Probability\,2011\, Vol. 39\, No. 4\, 1332&ndash\;1364\nDOI: 10
 .1214/10-AOP583
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR