Four-cycle free graphs, height functions, the pivot property and entropy minimality
نویسندگان
چکیده
منابع مشابه
Graphs of Functions and Vanishing Free Entropy
Suppose X = {x1, . . . , xn} is an n-tuple of selfadjoint elements in a tracial von Neumann algebra M . If z = z∗ ∈ M and for some y = y∗ in the von Neumann algebra generated by X δ0(y, z) < δ0(y) + δ0(z), then χ(X ∪ {z}) = −∞ (here χ and δ0 denote the microstates free entropy and free entropy dimension, respectively). In particular, if z lies in the von Neumann algebra generated by X , then χ(...
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Suppose that N is a diffuse, property T von Neumann algebra and X is an arbitrary finite generating set of selfadjoint elements for N. By using rigidity/deformation arguments applied to representations of N in ultraproducts of full matrix algebras, we deduce that the microstate spaces of X are asymptotically discrete up to unitary conjugacy. We use this description to show that the free entropy...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2016
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2015.88