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SUMMARY:The competitive spectral radius of families of nonexpansive mappin
 gs
DTSTART:20260129T130000Z
DTEND:20260129T140000Z
DTSTAMP:20260424T050800Z
UID:indico-event-15484@indico.math.cnrs.fr
DESCRIPTION:Speakers: Stéphane Gaubert (Inria Saclay & École Polytechniq
 ue)\n\nWe consider a new class of repeated zero-sum games in which the pay
 off is the escape rate of a switched dynamical system\, where at every sta
 ge\, the transition is given by a nonexpansive operator depending on the a
 ctions of both players. This generalizes to the two-player (and non-linear
 ) case the notion of joint spectral radius of a family of matrices. We sho
 w that the value of this game does exist\, and we characterize it in terms
  of an infinite dimensional non-linear eigenproblem. This provides a two-p
 layer analogue of Mañe's lemma from ergodic control. This also extends to
  the two-player case results of Kohlberg and Neyman (1981)\, Karlsson (200
 1)\, and Vigeral and the second author (2012)\, concerning the asymptotic 
 behavior of nonexpansive mappings. We discuss two special cases of this ga
 me: order preserving and positively homogeneous self-maps of a cone equipp
 ed with Funk's and Thompson's metrics\, and groups of translations. \n\nT
 his is based on arXiv:2410.21097\, with Marianne Akian and Loïc Marchesin
 i\, and on a followup work with Ian Morris\, 2505.22468 (CDC2025).\n\nhttp
 s://indico.math.cnrs.fr/event/15484/
LOCATION:E2290 (Tours)
URL:https://indico.math.cnrs.fr/event/15484/
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