Tempering chains achieve polynomial spectral gap lower bounds of order 11-12 for multimodal Gibbs measures without explicit energy landscape structure.
Ergodicity for SDEs and approx- imations: locally Lipschitz vector fields and degenerate noise
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Dissipative stochastic differential equations are mean-square dissipative, and their stability and bifurcations can be analyzed via linearised systems using deterministic methods.
Establishes stability bounds for SHK flows yielding dimension-free controls on log-likelihood ratios and divergences, then applies them to time-dependent Pure-DP and Approximate-DP certificates for exponential-mechanism samplers.
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Rapid convergence of tempering chains to multimodal Gibbs measures
Tempering chains achieve polynomial spectral gap lower bounds of order 11-12 for multimodal Gibbs measures without explicit energy landscape structure.
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Mean-square Stability and Bifurcations for Dissipative SDEs
Dissipative stochastic differential equations are mean-square dissipative, and their stability and bifurcations can be analyzed via linearised systems using deterministic methods.
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On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy
Establishes stability bounds for SHK flows yielding dimension-free controls on log-likelihood ratios and divergences, then applies them to time-dependent Pure-DP and Approximate-DP certificates for exponential-mechanism samplers.