Variational inference via Gaussian interacting particles in the Bures--Wasserstein geometry
Borghi, G
Carrillo, J
Proceedings of the International Conference on Machine Learning (PMLR 306)
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Von Neumann Equivalence Rigidity
Daniel Drimbe
(University of Iowa)
Abstract
The notion of measure equivalence for discrete groups was introduced by Gromov as a measurable counterpart to the geometric notion of quasi-isometry. Measure equivalence is closely connected to the theory of II_1 factors: if groups G and H are measure equivalent, then they admit free ergodic probability measure preserving actions whose associated von Neumann algebras are stably isomorphic. Also, two groups G and H are said to be W*-equivalent if their group von Neumann algebras are stably isomorphic.
More recently, an even coarser equivalence relation between groups, termed von Neumann equivalence, was introduced by Ishan, Peterson, and Ruth; it is implied by both measure equivalence and W*-equivalence. In joint work with Stefaan Vaes, we established a unique factorization theorem for direct products of hyperbolic groups up to von Neumann equivalence.
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