Date:
Wed, 12/11/202511:00-13:00
Zoom link: https://huji.zoom.us/j/81365228311?pwd=Y9EprDJoHmCHO93jw6qxhz9E1HZQhL.1
Meeting ID: 813 6522 8311
Passcode: 951667
Title: Generic sampling and invariant measures on the space of k-uniform hypergraphs.
Abstract: We prove a model-theoretic representation theorem for the distribution of an ergodic exchangeable k-uniform hypergraph: every such measure arises as the pushforward of the countably-iterated Morley product of a global Borel-definable Keisler measure over the countable universal homogeneous k-uniform hypergraph. We show this by starting with a Borel k-hypergraphon $W$ and constructing a Keisler measure $\mu_W$ such that generic sampling with respect to $\mu_W$ yields the same invariant measure as does the standard hypergraphon sampling procedure with respect to $W$. When k=2, our results give a new representation theorem for ergodic exchangeable graphs via Keisler measures over a monster model of the Rado graph. This work is joint with Nathanael Ackerman, Cameron Freer, James E. Hanson, and Rehana Patel.
Meeting ID: 813 6522 8311
Passcode: 951667
Title: Generic sampling and invariant measures on the space of k-uniform hypergraphs.
Abstract: We prove a model-theoretic representation theorem for the distribution of an ergodic exchangeable k-uniform hypergraph: every such measure arises as the pushforward of the countably-iterated Morley product of a global Borel-definable Keisler measure over the countable universal homogeneous k-uniform hypergraph. We show this by starting with a Borel k-hypergraphon $W$ and constructing a Keisler measure $\mu_W$ such that generic sampling with respect to $\mu_W$ yields the same invariant measure as does the standard hypergraphon sampling procedure with respect to $W$. When k=2, our results give a new representation theorem for ergodic exchangeable graphs via Keisler measures over a monster model of the Rado graph. This work is joint with Nathanael Ackerman, Cameron Freer, James E. Hanson, and Rehana Patel.