自由群保测度作用下马氏球平均的平均收敛性
Mean convergence of Markovian spherical averages for measure-preserving actions of the free group
摘要：
对于概率空间上有限生成的自由群的保测度作用，建立了马氏球平均的平均收敛性。我们赋予一组发电机与广义马尔可夫链，并建立在这种情况下，在温和的非退化假设随机阵$Π$定义我们的马尔可夫链的平均收敛的球形平均。等价地，我们建立了相应Markov算子的尾σ-代数的平凡性。这种收敛性以前只知道对称马尔可夫链，而在我们的文件中，确保收敛的条件是不等式，而不是等式，所以平均球平均收敛的马尔可夫链建立了一个更大的类。
英文摘要：
Mean convergence of Markovian spherical averages is established for a measure-preserving action of a finitely-generated free group on a probability space. We endow the set of generators with a generalized Markov chain and establish the mean convergence of resulting spherical averages in this case under mild nondegeneracy assumptions on the stochastic matrix $Π$ defining our Markov chain. Equivalently, we establish the triviality of the tail sigma-algebra of the corresponding Markov operator. This convergence was previously known only for symmetric Markov chains, while the conditions ensuring convergence in our paper are inequalities rather than equalities, so mean convergence of spherical averages is established for a much larger class of Markov chains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
