发表机构
University of Edinburgh; National Technical University of Athens; Athena/Archimedes Research Centre（爱丁堡大学; 雅典国立技术大学; Athena/Archimedes 研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非凸且非梯度-Lipschitz 势的矩阵空间 Gibbs 采样，提出非二次动能驱动的欠阻尼 Langevin 系统，实现动量预处理，证明测度不变性与指数收敛，并保证离散化算法的稳定性。
AI 中文摘要
我们考虑从矩阵空间上的 Gibbs 分布中采样的问题，其中势能既非凸也非全局梯度-Lipschitz。我们引入一族非二次动能，导致一个新的欠阻尼 Langevin 系统，具有动量预处理，其中动能的梯度充当动量的平滑谱驯化。我们证明，在这些对势的放宽假设下，所得动力学保持目标 Gibbs 测度不变，并建立了在加权全变差距离下指数收敛到平衡。最后，我们表明相应的 Euler-Maruyama 离散化允许时间一致的矩界，无需修改势梯度，这确保了所得采样算法的稳定性。
英文摘要
We consider the problem of sampling from Gibbs distributions on matrix spaces whose potential energies are neither convex nor globally gradient-Lipschitz. We introduce a family of non-quadratic kinetic energies that lead to a new underdamped Langevin system with momentum preconditioning, in which the gradient of the kinetic energy acts as a smooth spectral taming of the momentum. We prove that, under these relaxed assumptions on the potential, the resulting dynamics leaves the target Gibbs measure invariant, and we establish exponential convergence to equilibrium in a weighted total variation distance. Finally, we show that the corresponding Euler-Maruyama discretization admits moment bounds that are uniform in time, without any modification of the potential gradient, which ensures the stability of the resulting sampling algorithm.
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