Dynamical Bulk Scaling Limit of Gaussian Unitary Ensembles and Stochastic Differential Equation Gaps
Dynamical Bulk Scaling Limit of Gaussian Unitary Ensembles and Stochastic Differential Equation Gaps
复制标题
高斯酉系综的动态体尺度极限和随机微分方程间隙
DOI：
10.1007/s10959-018-0816-2
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发表时间：
2018
影响因子：
0.8
通讯作者：
Osada Hirofumi
中科院分区：
文献类型：
--
作者：
Kawamoto Yosuke;Osada Hirofumi
高斯酉系综的 N 粒子系统的分布在体积尺度限制下收敛于正弦点过程。这些缩放比例由半圆分布支持的宏观位置参数化。限制始终是正弦点过程，并且与行列式核的膨胀的宏观位置无关。我们证明了这一事实的动态对应。我们证明了由随机微分方程（SDE）给出的 N 粒子系统的解收敛于无限维戴森模型的解。我们证明了极限无限维SDE（ISDE），称为戴森模型，与宏观位置无关，而N粒子SDE在极限上依赖于ISDE，并且与ISDE不同。
The distributions ofN-particle systems of Gaussian unitary ensembles converge to Sinepoint processes under bulk scaling limits. These scalings are parameterized by a macro-positionin the support of the semicircle distribution. The limits are always Sinepoint processes and independent of the macro-positionup to the dilations of determinantal kernels. We prove a dynamical counterpart of this fact. We prove that the solution to theN-particle system given by a stochastic differential equation (SDE) converges to the solution of the infinite-dimensional Dyson model. We prove that the limit infinite-dimensional SDE (ISDE), referred to as Dyson’s model, is independent of the macro-position, whereas theN-particle SDEs depend onand are different from the ISDE in the limit whenever.