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Title: The relative f -invariant and non-uniform random sofic approximations
Abstract The f -invariant is an isomorphism invariant of free-group measure-preserving actions introduced by Lewis Bowen, who first used it to show that two finite-entropy Bernoulli shifts over a finitely generated free group can be isomorphic only if their base measures have the same Shannon entropy. Bowen also showed that the f -invariant is a variant of sofic entropy; in particular, it is the exponential growth rate of the expected number of good models over a uniform random homomorphism. In this paper we present an analogous formula for the relative f -invariant and use it to prove a formula for the exponential growth rate of the expected number of good models over a random sofic approximation which is a type of stochastic block model.  more » « less
Award ID(s):
1855694
PAR ID:
10398463
Author(s) / Creator(s):
Date Published:
Journal Name:
Ergodic Theory and Dynamical Systems
ISSN:
0143-3857
Page Range / eLocation ID:
1 to 38
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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