The relative f -invariant and non-uniform random sofic approximations
The relative f -invariant and non-uniform random sofic approximations
复制标题
相对 f 不变和非均匀随机 sofic 近似
DOI：
10.1017/etds.2022.27
复制
发表时间：
2022
影响因子：
0.9
通讯作者：
SHRIVER, CHRISTOPHER
中科院分区：
文献类型：
--
作者：
SHRIVER, CHRISTOPHER
f-不变量是刘易斯·鲍文（Lewis Bowen）引入的自由群保测度作用的同构不变量，他首先用它证明了两个有限熵的伯努利移位只有在它们的基测度具有相同的香农熵时才能同构。Bowen还证明了f-不变量是sofic熵的一个变体;特别地，它是均匀随机同态上的好模型的预期数量的指数增长率。本文给出了相对f-不变量的一个类似公式，并利用它证明了一类随机块模型的随机sofic近似上的期望好模型数的指数增长率公式。
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.