论文标题
彼得森的随机矩阵方法 - 猜想
A random matrix approach to the Peterson-Thom conjecture
论文作者
论文摘要
Peterson-Thom猜想断言，自由组因子的任何弥漫性，可及的亚代词都包含在唯一的最大最大amenable子代数中。这种猜想是由POPA变形/刚性理论的相关结果和Peterson-Thom在l^{2} -betti数字上的结果所激发的。我们通过制定一种猜想是对Haagerup-thorbjornsen定理的自然概括的猜想来提出了这种猜想的方法，该方法的有效性暗示了Peterson-Thom Thomthom Thomthom，这是对Haagerup-thorbjornsen定理的自然概括。这种随机的矩阵猜想与Collins-Guionnet-Parraud的最新工作有关。
The Peterson-Thom conjecture asserts that any diffuse, amenable subalgebra of a free group factor is contained in a unique maximal amenable subalgebra. This conjecture is motivated by related results in Popa's deformation/rigidity theory and Peterson-Thom's results on L^{2}-Betti numbers. We present an approach to this conjecture in terms of so-called strong convergence of random matrices by formulating a conjecture which is a natural generalization of the Haagerup-Thorbjornsen theorem whose validity would imply the Peterson-Thom conjecture. This random matrix conjecture is related to recent work of Collins-Guionnet-Parraud.
