论文标题
相对的F不变和不均匀的随机SOFIC近似
The relative f-invariant and non-uniform random sofic approximations
论文作者
论文摘要
$ f $ invariant是由刘易斯·鲍恩（Lewis Bowen）在[Arxiv：0802.4294]中引入的自由组量度衡量措施动作的同构不变的，在那里它被用来证明两个有限的伯努尔（Bernoulli）在有限生成的自由群体上只能是同样的基础量表，而同样的基本量表则是Shannon shannon shannon shannon shannon shannon shannon shannon shannon shannnon shann nann。在[arxiv：0902.0174]中，鲍恩（Bowen）表明$ f $ invariant是Sofic熵的变体；特别是，在均匀的随机同态同构中，良好模型的预期数量的指数增长率。 在本文中，我们为相对$ f $ invariant提供了一个类似的公式，并使用它来证明在随机的SOFIC近似值上，这是一种随机模型，这是一种随机模型，这是一种预期的良好模型的指数增长率。
The $f$-invariant is an isomorphism invariant of free-group measure-preserving actions introduced by Lewis Bowen in [arXiv:0802.4294], where it was used 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. In [arXiv:0902.0174] Bowen 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.
