论文标题
超纤维，正式动作和熵
Ultralimits, Amenable actions and Entropy
论文作者
论文摘要
在本文中，我们表明，对于任何符合性的作用，Furstenberg熵的最小价值（遵循所有措施，而不是限制固定的措施）与该组本身的作用相同。使用ADAMS的边界舒适性结果，这使我们能够在自由组边界中的所有度量类别上计算熵的最小值。双曲线群在其Gromov边界上的作用证明了类似的结果。我们的主要工具是对小组依赖的矩阵值随机步行的泊松边界的超级映射实现。这扩展并完善了Y. Shalom先前论文的结果和工具。
In this paper we show that the minimal value of Furstenberg entropy (along all measures, not restricting to stationary ones) for any amenable action is the same as for the action of the group on itself. Using the boundary amenability result of Adams, this allows us to compute the minimal value of the entropy over all the measure classes in the boundary of the free group. Similar results are proved for the action of a hyperbolic group on its Gromov boundary. Our main tool is an ultralimit realization of the Poisson boundary of a time dependent matrix-valued random walk on the group. This extends and refines the results and tools of previous paper of the author with Y. Shalom.
