In this work, we study the number of small eigenvalues and the convergence to the equilibrium of the Bouncy Particle Sampler process and the zigzag process generators in the small temperature regime. Such processes, which fall in the class of Piecewise Deterministic Markov Processes, are non-diffusive and non-reversible. They have recently been used a lot for simulation issues, falling in the domain of Markov chain Monte Carlo method, due to their numerically observed astonishing performances. Nevertheless, they are far from being theoretically understood, in particular at the spectral level, which is the scope of our study.

中文翻译：

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小区间温度下低分段特征值和某些分段确定性马尔可夫过程生成器的收敛性

在这项工作中，我们研究了小特征值的数量以及在小温度范围内弹性粒子采样器过程和之字形过程生成器到平衡的收敛性。属于分段确定性马尔可夫过程类的此类过程是不可扩散且不可逆的。由于它们在数值上的惊人表现，它们最近在模拟问题中得到了广泛使用，属于马尔可夫链蒙特卡罗方法的范畴。然而，它们还远没有得到理论上的理解，特别是在光谱水平上，这是我们研究的范围。