CRM: Centro De Giorgi
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Seminari di Sistemi Dinamici Olomorfi 2018-2019

seminar: Nonsingular Bernoulli

speaker: Oleksandr Ivanovych Danilenko (Institute for Low Temperature Physics & Engineering of National Academy of Sciences of Ukraine)

abstract: Let G be an amenable discrete countable infinite group, A a finite set, and (μg)g2G a family of probability measures on A such that infg2G mina2A μg(a) > 0. It is shown (among other results) that if the Bernoulli shiftwise action of G on the infinite product spaceNg2G(A, μg) is nonsingular and conservative then it is weakly mixing. This answers in positive a question by Z. Kosloff who proved recently that the conservative Bernoulli Zd-actions are ergodic. As a byproduct, we prove a weak version of the pointwise ratio ergodic theorem for nonsingular actions of G.

Wed 10 Apr, 14:30 - 15:30, Sala Conferenze Centro De Giorgi
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