论文标题
一般$β\ geq 1 $的dyson布朗运动的边缘缩放限制
Edge scaling limit of Dyson Brownian motion at equilibrium for general $β\geq 1$
论文作者
论文摘要
对于一般$β\ geq 1 $，我们考虑以平衡状态Dyson Brownian运动，并证明了极限粒子在极限$ n \ to \ ftty $中的连续样品路径集合中的收敛。对于每个固定时间，此合奏被分布成通风$_β$随机点字段。我们证明了限制过程的增量是局部布朗尼人。当$β> 1 $ $时，我们证明在减去布朗运动后，对于任何$ r <1-（1+β）^{ - 1} $，样本路径几乎肯定是本地$ r $ -h {Ö} lder。此外，对于所有$β\ geq 1 $，我们表明限制过程在弱的意义上解决了SDE。当$β= 2 $时，此限制过程是通风线的集合。
For general $β\geq 1$, we consider Dyson Brownian motion at equilibrium and prove convergence of the extremal particles to an ensemble of continuous sample paths in the limit $N \to \infty$. For each fixed time, this ensemble is distributed as the Airy$_β$ random point field. We prove that the increments of the limiting process are locally Brownian. When $β>1$ we prove that after subtracting a Brownian motion, the sample paths are almost surely locally $r$-H{ö}lder for any $r<1-(1+β)^{-1}$. Furthermore for all $β\geq 1$ we show that the limiting process solves an SDE in a weak sense. When $β=2$ this limiting process is the Airy line ensemble.
