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SUMMARY:Haojie Ren (Technion)
DTSTART:20241126T130000Z
DTEND:20241126T140000Z
DTSTAMP:20260423T021328Z
UID:OWNS/137
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/137/">T
 he dimension of Bernoulli convolutions in $\\mathbb{R}^d$</a>\nby Haojie R
 en (Technion) as part of One World Numeration seminar\n\n\nAbstract\nFor $
 (\\lambda_{1}\,\\dots\,\\lambda_{d})=\\lambda\\in(0\,1)^{d}$ with $\\lambd
 a_{1}>\\cdots>\\lambda_{d}$\,\ndenote by $\\mu_{\\lambda}$ the Bernoulli c
 onvolution associated to\n$\\lambda$. That is\, $\\mu_{\\lambda}$ is the d
 istribution of the random\nvector $\\sum_{n\\ge0}\\pm\\left(\\lambda_{1}^{
 n}\,\\dots\,\\lambda_{d}^{n}\\right)$\,\nwhere the $\\pm$ signs are chosen
  independently and with equal weight.\nAssuming for each $1\\le j\\le d$ t
 hat $\\lambda_{j}$ is not a root\nof a polynomial with coefficients $\\pm1
 \,0$\, we prove that the dimension\nof $\\mu_{\\lambda}$ equals $\\min\\{ 
 \\dim_{L}\\mu_{\\lambda}\,d\\} $\,\nwhere $\\dim_{L}\\mu_{\\lambda}$ is th
 e Lyapunov dimension. This is a joint work with Ariel Rapaport.\n
LOCATION:https://researchseminars.org/talk/OWNS/137/
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