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SUMMARY:Multitype Galton-Watson processes in random environment and produc
 ts of random operators
DTSTART:20251007T075000Z
DTEND:20251007T085000Z
DTSTAMP:20260915T120200Z
UID:indico-event-14853@indico.math.cnrs.fr
DESCRIPTION:Speakers: Maxime Ligonnière (IMT)\n\nGalton-Watson processes 
 form a large class of discrete time population models\, in which individua
 ls engage in an asexual and random reproduction\, without interacting with
  each other. In this talk\, we study processes of this class in which each
  individual has a type and the reproduction of individuals is affected by 
 a changing environment represented by a stationary and ergodic process. Na
 mely\, the probability distribution of the offpsring of an individual depe
 nds both on its type and the state of the environment at the time he lives
 . The study of such a process relies on the understanding of its quenched 
 mean\, that is\, the mean of the population conditionally on the environme
 ntal process. This mean is linked to a product of random positive linear o
 perators which act on some measures and functions space. In the case where
  there is only a finite number of possible types\, these operators are mer
 ely positive matrices. The rich theory of products of random matrices\, in
 tiated in the 1960s\, has allowed to obtain precise results on the associa
 ted Galton-Watson processes in the last decades. We focus here on the case
  of an infinite set of possible types. We start by obtaining a ergodicity 
 result for the associated products of operators\, from which we deduce suf
 ficient condition for almost sure extinction\, as well as a description of
  the surviving population when there is one\, under the form of a Kesten-S
 tigum-type theorem. \n\nhttps://indico.math.cnrs.fr/event/14853/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/14853/
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