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SUMMARY:Ofir Gorodetsky (University of Oxford)
DTSTART:20240529T150000Z
DTEND:20240529T160000Z
DTSTAMP:20260418T065732Z
UID:LNTS/129
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/129/">M
 artingale central limit theorems for weighted sums of random multiplicativ
 e functions</a>\nby Ofir Gorodetsky (University of Oxford) as part of Lond
 on number theory seminar\n\nLecture held in Room K0.18 King's Building\, K
 ing's College London (Strand Campus).\n\nAbstract\nA random multiplicative
  function is a multiplicative function alpha(n) such that its values on pr
 imes\, (alpha(p))_(p=2\,3\,5\,...)\, are i.i.d. random variables. The simp
 lest example is the Steinhaus function\, which is a completely multiplicat
 ive function with alpha(p) uniformly distributed on the unit circle. A bas
 ic question in the field is finding the limiting distribution of the (norm
 alized) sum of alpha(n) from n=1 to n=x\, possibly restricted to a subset 
 of integers of interest. This question is currently resolved only in a few
  cases. We shall describe ongoing work where we are able to find the limit
 ing distribution in many new instances of interest. The distribution we fi
 nd is not gaussian\, in contrast to all previous works. This is joint work
  with Mo Dick Wong (Durham University).\n
LOCATION:https://researchseminars.org/talk/LNTS/129/
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