The spherical ensemble is a well-known ensemble of N repulsive points on the two-dimensional sphere, which can realized in various ways (as a random matrix ensemble, a determinantal point process, a Coulomb gas, a Quantum Hall state...). Here we show that the spherical ensemble enjoys nearly optimal convergence properties from the point of view of numerical integration. More precisely, it is shown that the numerical integration rule corresponding to N nodes on the two-dimensional sphere sampled in the spherical ensemble is, with overwhelming probability, nearly a quasi-Monte-Carlo design in the sense of Brauchart-Saff-Sloan-Womersley (for any smoothness parameter s less than or equal to two). The key ingredient is a new explicit concentration of measure inequality for the spherical ensemble.

翻译：球形集合是二维球体上众所周知的令人厌恶的共点集合点, 可以通过多种方式实现( 随机矩阵组合、 决定性点进程、 库伦布气体、 量子大厅状态... ) 。 这里我们显示, 从数字整合的角度来看, 球形组合具有几乎最佳的趋同特性。 更确切地说, 已经显示, 与在球形组合中抽样的二维球体上的N节相对应的数字集成规则, 极有可能是布劳查特- 萨夫- 斯洛安- 沃默斯利( 任何光滑度参数小于或等于两个) 意义上的准蒙特- 卡洛设计。 关键成分是球形组合中测量不平等的新明显集中。