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SUMMARY:Reinforced Galton-Watson processes. - Jean Bertoin (Universität Z
 ürich)
DTSTART:20240711T081500Z
DTEND:20240711T091500Z
UID:TALK215590@talks.cam.ac.uk
DESCRIPTION:In a reinforced Galton-Watson process with&nbsp\; reproduction
  law $\\nu$ and memory parameter $q\\in(0\,1)$\, the number of children of
  a typical individual either\, with probability$q$\, repeats that of one o
 f its forebears picked uniformly at random\, or\, with complementary proba
 bility&nbsp\; $1-q$\, is given by an independent sample from $\\nu$. We es
 timate the average size of the population at a large generation\, and in p
 articular\, we determine explicitly the&nbsp\; Malthusian growth rate in t
 erms of $\\nu$ and $q$. Our approach via the analysis of transport equatio
 ns&nbsp\; owes much to works by Flajolet and co-authors.\nThis talk is bas
 ed on joint works with Bastien Mallein (Toulouse)
LOCATION:Seminar Room 1\, Newton Institute
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