论文标题
$β$增强的操作员级别难以过渡
Operator level hard-to-soft transition for $β$-ensembles
论文作者
论文摘要
$β$增强的柔软和硬边缩放极限可以被描述为某些随机Sturm-Liouville操作员的光谱。已经表明，通过调整硬边过程的参数，可以将软边过程作为缩放限制获得。我们证明，可以在相应的随机操作员的级别上实现此限制。更准确地说，随机操作员可以以某种方式耦合，以便硬边算子的缩放版本收敛到软边算子A.S.从规范的意义上讲。
The soft and hard edge scaling limits of $β$-ensembles can be characterized as the spectra of certain random Sturm-Liouville operators. It has been shown that by tuning the parameter of the hard edge process one can obtain the soft edge process as a scaling limit. We prove that this limit can be realized on the level of the corresponding random operators. More precisely, the random operators can be coupled in a way so that the scaled versions of the hard edge operators converge to the soft edge operator a.s. in the norm resolvent sense.
