Samuel Mellick, "Point processes on groups I: factor graphs and the Palm equivalence relation"

mardi 10 nov. 2020, 10:15 → 11:45 Europe/Paris

Point processes are random subsets of spaces. We study invariant point processes on topological groups, which form an interesting class of probability measure preserving actions. In fact, *every* free p.m.p. action of a locally compact group is isomorphic to a point process. 

This talk will be a crash course on point processes for nonprobabilists. I'll explain how to associate a p.m.p. countable Borel equivalence relation to point processes, and how this gadget governs the graphs that "live on" the point process. We'll use this to give a point process characterisation of amenability, and also to construct new examples of p.m.p. cbers that cannot be freely generated by any action of a discrete group with the help of Popa's cocycle superrigidity and "extra head schemes".

The material in this talk will lay the groundwork for my next talk about the cost of point processes, in which I'll explain why the Poisson point process has maximal cost and how to exploit this to give the first nontrivial examples of nondiscrete groups with fixed price.