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SUMMARY:Mykola Pratsiovytyi (Mykhailo Drahomanov Ukrainian State Universit
 y\; Institute of Mathematics\, Natl. Acad. Sci. Ukraine)
DTSTART:20241010T123000Z
DTEND:20241010T140000Z
DTSTAMP:20260423T005740Z
UID:fran/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/fran/53/">Pr
 obability distributions on fractal curves of spiderweb type</a>\nby Mykola
  Pratsiovytyi (Mykhailo Drahomanov Ukrainian State University\; Institute 
 of Mathematics\, Natl. Acad. Sci. Ukraine) as part of Семінар з ф
 рактального аналізу / Fractal analysis seminar\n\n\nAbst
 ract\nIn the talk\, we consider a complex-valued random variable\n\\[\n  \
 \tau = \\sum_{n=1}^\\infty \\frac{2 \\varepsilon_{\\tau_n}}{3^n}\,\n\\]\nw
 here $(\\tau_n)$ is a sequence of independent random variables taking the 
 values $0$\, $1$\, …\, $6$ with the probabilities $p_{0n}$\, $p_{1n}$\, 
 …\, $p_{6n}$\, respectively\, and $\\varepsilon_0$\, $\\varepsilon_1$\, 
 …\, $\\varepsilon_5$ are the $6$th roots of unity\, $\\varepsilon_6 = 0$
 . Structural\, spectral\, topological\, metric\, and fractal properties of
  distribution of this random variable are studied.\n\nWe prove that the se
 t of values of the random variable $\\tau$ is a self-similar fractal curve
  of spiderweb type with dimension $\\log_3 7$. Its outline is the Koch sno
 wflake.\n\nThe Lebesgue structure of distribution of $\\tau$ is also studi
 ed in detail.\n\nIn the case of identically distributed random variables $
 \\tau_n$ we establish that the spectrum of distribution of $\\tau$ is a se
 lf-similar fractal and essential support of density is a fractal set of Be
 sicovitch–Eggleston type.\n
LOCATION:https://researchseminars.org/talk/fran/53/
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