Universality of the Stochastic Bessel Operator
Universality of the Stochastic Bessel Operator
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DOI：
10.1007/s00440-018-0888-z
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发表时间：
2016-10
影响因子：
2
通讯作者：
B. Rider;Patrick Waters
中科院分区：
文献类型：
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作者：
B. Rider;Patrick Waters
我们建立了一般β系综在硬边的普适性，假设：背景势V是一个多项式，使得是强凸的，和“维数差”参数。该方法依赖于相应的三对角矩阵模型，表明其适当的连续标度极限是由随机贝塞尔算子。正如Edelman和萨顿（J Stat Phys 127：1121-1165，2007）所阐述的，以及Ramírez和Rider（Commun Math Phys 288：887-906，2009）所严格建立的，后者描述了线性势和所有（经典的“β-Laguerre”系综）情况下的硬边。
We establish universality at the hard edge for general beta ensembles assuming that: the background potentialVis a polynomial such thatis strongly convex,, and the “dimension-difference” parameter. The method rests on the corresponding tridiagonal matrix models, showing that their appropriate continuum scaling limit is given by the Stochastic Bessel Operator. As conjectured in Edelman and Sutton (J Stat Phys 127:1121–1165, 2007) and rigorously established in Ramírez and Rider (Commun Math Phys 288:887–906, 2009), the latter characterizes the hard edge in the case of linear potential and all(the classical “beta-Laguerre” ensembles).