The Bessel point process is a rigid point process on the positive real line and its conditional measure on a bounded interval [Formula: see text] is almost surely an orthogonal polynomial ensemble. In this paper, we show that if [Formula: see text] tends to infinity, one almost surely recovers the Bessel point process. In fact, we show this convergence for a deterministic class of probability measures, to which the conditional measure of the Bessel point process almost surely belongs.

中文翻译：

---

贝塞尔点过程条件测度的普遍性

贝塞尔点过程是正实线上的刚性点过程，它在有界区间上的条件测度[公式：见正文]几乎肯定是正交多项式系综。在本文中，我们展示了如果 [公式：见正文] 趋于无穷大，几乎可以肯定地恢复贝塞尔点过程。事实上，我们展示了一类确定性概率测度的收敛性，贝塞尔点过程的条件测度几乎肯定属于该类。