论文标题
软边和硬边过程的全球刚度和指数时刻
Global rigidity and exponential moments for soft and hard edge point processes
论文作者
论文摘要
我们为通用确定点过程建立了尖锐的全球刚度上限，描述了随机矩阵的边缘特征值。为此，我们首先获得一个一般结果，该结果可以应用于具有最小（或最大）点的一般（不一定是确定性）点过程：它允许从该过程计数函数的指数矩中推断出全局刚度上限。通过将其与已知的通风和贝塞尔点过程中的已知指数力矩渐近学结合起来，我们在通风点过程的全球刚度方面提高了最著名的上限，并为贝塞尔点过程获得了新的全球刚性结果。 其次，我们为Wright的广义Bessel过程和Meijer-$ \ Mathrm {G} $进程获得指数力矩渐近学，直到恒定术语。作为一个直接的结果，我们为相关计数函数的期望和差异获得了新的结果。此外，通过将这些渐近学与我们的一般刚性定理相结合，我们为这些点过程获得了新的全球刚性上限。
We establish sharp global rigidity upper bounds for universal determinantal point processes describing edge eigenvalues of random matrices. For this, we first obtain a general result which can be applied to general (not necessarily determinantal) point processes which have a smallest (or largest) point: it allows to deduce global rigidity upper bounds from the exponential moments of the counting function of the process. By combining this with known exponential moment asymptotics for the Airy and Bessel point processes, we improve on the best known upper bounds for the global rigidity of the Airy point process, and we obtain new global rigidity results for the Bessel point process. Secondly, we obtain exponential moment asymptotics for the Wright's generalized Bessel process and the Meijer-$\mathrm{G}$ process, up to and including the constant term. As a direct consequence, we obtain new results for the expectation and variance of the associated counting functions. Furthermore, by combining these asymptotics with our general rigidity theorem, we obtain new global rigidity upper bounds for these point processes.
