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LA Probability Forum

Thursday, October 5, 2023
3:00pm to 4:00pm
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Poisson-Voronoi tessellations and fixed price in higher rank
Amanda Wilkins, Department of Mathematics, University of Texas, Austin,

USC, Kaprelian (KAP) 414

We overview the cost of a group action, which measures how much information is needed to generate its induced orbit equivalence relation, and the ideal Poisson-Voronoi tessellation (IPVT), a new random limit with interesting geometric features. In recent work, we use the IPVT to prove all measure preserving and free actions of a higher rank semisimple Lie group on a standard probability space have cost 1, answering Gaboriau's fixed price question for this class of groups. We sketch a proof, which relies on some simple dynamics of the group action and the definition of a Poisson point process. No prior knowledge on cost, IPVTs, or Lie groups will be assumed. This is joint work with Mikolaj Fraczyk and Sam Mellick.

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