Persi Diaconis (Stanford)

The process of 'carries' when adding a list of numbers leads to a Markov chain with an "amazing" transition matrix. This same matrix comes up in shuffling cards and in taking sections of generating functions. There are also neatly associated determinental point processes. This is joint work with Jason Fulman and Alexei Borodine.
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Dan Stroock (MIT)

I will begin by reminding those who do know, and telling those who don't, what Lenard Gross's theory of abstract Wiener space is about. Once I have done this, I will formulate, prove, and discuss in the context of abstract Wiener spaces an ergodic theorem which, in essence, is due to Irving Segal.
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Vladislav Kargin (Stanford)

Lyapunov exponents are interesting mathematical object that can be used to gauge the stability and complexity of a dynamical system. The study of properties of Lyapunov exponents of random matrices has been initiated in seminal papers by Furstenberg, Kesten, Oseledec, and Newman. In this talk, I will describe a generalization of the results on random matrix products to the case of products of free infinitely-dimensional operators. In particular, I will discuss the speed of growth in the norm of free operator products, possible variants of the definition of Lyapunov exponents, and the tools that are available for their calculation.
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