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Will be on Zoom<\/strong> https:\/\/us02web.zoom.us\/j\/83337601824<\/a> Time: 14:00<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n Abstract: Pointwise ergodic theorems provide a bridge between the global behaviour of the dynamical system and the local combinatorial statistics of the system at a point. Such theorems have been proven in different contexts, but typically for actions of semigroups on a probability space. Dating back to Birkhoff (1931), the first known pointwise ergodic theorem states that for a measure-preserving ergodic transformation T on a probability space, the mean of a function (its global average) can be approximated by taking local averages of the function at a point x over finite sets in the forward-orbit of x, namely {x, T x, …, T^nx}. Almost a century later, we revisit Birkhoff’s theorem and turn it backwards, showing that the averages along trees of possible pasts also approximate the global average. This backward theorem for a single transformation surprisingly has applications to actions of free groups, which we will also discuss. This is joint work with Jenna Zomback.<\/p>\n","protected":false},"excerpt":{"rendered":" Will be on Zoom https:\/\/us02web.zoom.us\/j\/83337601824 Time: 14:00 Abstract: Pointwise ergodic theorems provide a bridge between the global behaviour of the dynamical system and the local combinatorial statistics of the system at a point. Such theorems have been proven in different contexts, but…
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