A note on partial rejection sampling for the hard disks model in the plane

Perfect simulation of the Hard Disks Model by Partial Rejection Sampling

We present a perfect simulation of the hard disks model via the partial rejection sampling method. Provided the density of disks is not too high, the method produces exact samples in $O(\log n)$ rounds, and total time $O(n)$, where $n$ is the expected number of disks. The method extends easily to the hard spheres model in $d>2$ dimensions. In order to apply the partial rejection method to this continuous setting, we provide an alternative perspective of its correctness and run-time analysis that is valid for general state spaces.

Rejection and Importance Sampling based Perfect Simulation for Gibbs hard-sphere models

Coupling from the past (CFTP) methods have been used to generate perfect samples from finite Gibbs hard-sphere models, an important class of spatial point processes, which is a set of spheres with the centers on a bounded region that are distributed as a homogeneous Poisson point process (PPP) conditioned that spheres do not overlap with each other. We propose an alternative importance sampling based rejection methodology for the perfect sampling of these models. We analyze the asymptotic expected running time complexity of the proposed method when the intensity of the reference PPP increases …

A note on normal matrix ensembles at the hard edge

We investigate how the theory of quasipolynomials due to Hedenmalm and Wennman works in a hard edge setting and obtain as a consequence a scaling limit for radially symmetric potentials.

关于LUE的最小eigenvalue分布在硬边展开的一个注记

A note on the expansion of the smallest eigenvalue distribution of the LUE at the hard edge

在最近的一篇论文中，Edelman、Guionnet和Péché在硬边标度极限中，对$n$阶拉盖尔酉系综（LUE）的最小特征值分布给出了一个特殊的$n^{-1}$修正项：具体地说，极限分布的导数，即密度，出现在该修正项中。我们给出了一个简短的证明，通过修改硬边缩放，以实现最佳的$O(n^{-2})$收敛速率的最小特征值分布。导数的出现随后是次优的标准硬边缩放的泰勒展开。我们涉及的$n^{-1}$校正项进一步的对数导数的贝塞尔内核弗雷德霍姆行列式在工作的特雷西和Widom。