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UID:782@lincs.fr
DTSTART;TZID=Europe/Paris:20230925T140000
DTEND;TZID=Europe/Paris:20230925T170000
DTSTAMP:20230922T132037Z
URL:https://www.lincs.fr/events/michel-davydovs-phd-thesis-defense-dynamiq
 ues-markoviennes-a-base-de-processus-ponctuels-et-leurs-applications/
SUMMARY:Phd Thesis Defense : Dynamiques markoviennes à base de processus
 ponctuels et leurs applications
DESCRIPTION:In this thesis\, we are interested in mathematical models of
 phenomena that can be interpreted as network dynamics. This includes for
 example neuron population models in which neurons interact at random times
 with their neighbors or epidemics propagation where infected or susceptible
 individuals move from town to town. The mathematical description of such
 phenomena generally requires a compromise between physical or biological
 relevance and mathematical tractability. The main focus of this work is the
 elaboration of mathematical proofs to justify the introduction of models
 taking into account the geometry of the underlying networks whilst
 preserving tractability. The main mathematical tool for that purpose is the
 replica-mean-field\, which consists in copies of the studied network
 between which interactions are routed randomly. The main results of this
 thesis concern the behavior of such a dynamical system when the number of
 replicas goes to infinity. In various settings\, we show that it concerges
 to dynamics under the Poisson Hypothesis\, that is\, interaction times are
 replaced by independent Poisson processes\, which allows to obtain closed
 forms in certain models.
CATEGORIES:PhD Defense
LOCATION:Inria\, salle Jacque-Louis Lion\, 2 rue Simone Iff\, Paris\, 75012
 \, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=2 rue Simone Iff\, Paris\,
 75012 \, France;X-APPLE-RADIUS=100;X-TITLE=Inria\, salle Jacque-Louis
 Lion:geo:0,0
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