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SUMMARY:Younès Tierce (Université de Rouen Normandie)
DTSTART:20211109T140000Z
DTEND:20211109T143000Z
DTSTAMP:20260423T052925Z
UID:OWNS/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/68/">Ex
 tensions of the random beta-transformation</a>\nby Younès Tierce (Univers
 ité de Rouen Normandie) as part of One World Numeration seminar\n\n\nAbst
 ract\nLet $\\beta \\in (1\,2)$ and $I_\\beta := [0\,\\frac{1}{\\beta-1}]$.
  Almost every real number of $I_\\beta$ has infinitely many expansions in 
 base $\\beta$\, and the random $\\beta$-transformation generates all these
  expansions. We present the construction of a "geometrico-symbolic" extens
 ion of the random $\\beta$-transformation\, providing a new proof of the e
 xistence and unicity of an absolutely continuous invariant probability mea
 sure\, and an expression of the density of this measure. This extension sh
 ows off some nice renewal times\, and we use these to prove that the natur
 al extension of the system is a Bernoulli automorphism.\n
LOCATION:https://researchseminars.org/talk/OWNS/68/
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