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SUMMARY:A family of functional inequalities: Lojasiewicz inequalities and
displacement convex functions
DTSTART;VALUE=DATE-TIME:20181112T083000Z
DTEND;VALUE=DATE-TIME:20181112T093000Z
DTSTAMP;VALUE=DATE-TIME:20220128T024404Z
UID:indico-contribution-3346@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jérôme Bolte (TSE)\nFor displacement convex functi
onals in the probability space equipped with the Monge-Kantorovich metric
we prove the equivalence between the gradient and functional type Łojasie
wicz inequalities. We also discuss the more general case of λ-convex func
tions and we provide a general convergence theorem for the corresponding g
radient dynamics. Specialising our results to the Boltzmann entropy\, we r
ecover Otto-Villani's theorem asserting the equivalence between logarithmi
c Sobolev and Talagrand's inequalities. The choice of power-type entropies
shows a new equivalence between Gagliardo-Nirenberg inequality and a nonl
inear Talagrand inequality. Some nonconvex results and other types of equi
valences are discussed.\n\nhttps://indico.math.cnrs.fr/event/3779/contribu
tions/3346/
LOCATION:Toulouse School of Economics Bât S\, amphi MS001
URL:https://indico.math.cnrs.fr/event/3779/contributions/3346/
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