We establish a spectral gap for Continuum Glauber dynamics on the hard sphere model assuming strong spatial mixing, thereby extending the range of parameters in which Continuum Glauber is provably rapidly mixing. To do this, we introduce continuous extensions of spectral independence and negative fields localization. Our techniques apply to general Gibbs point processes with finite-range repulsive pair potentials. As a corollary, we improve the threshold up to which packings of a fixed number of spheres can be sampled from a bounded domain.

翻译：在假设强空间混合的条件下，我们为硬球模型上的连续Glauber动力学建立了谱间隙，从而扩展了连续Glauber动力学被证明快速混合的参数范围。为此，我们引入了谱独立性和负场局部化的连续扩展。我们的技术适用于具有有限程排斥对势的一般吉布斯点过程。作为推论，我们改进了从有界域中采样固定数量球体堆积的阈值上限。