Spectral gaps for the O-U/Stochastic heat processes on path space over a Riemannian manifold with boundary

2018/12/05 by Bo Wu, Wu, Bo
Mathematics · #60D05 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Probability (math.PR) #math.PR #msc:60D05

paper · pdf · doi:10.48550/arxiv.1812.01826

arxiv created 2018/12/05 · openalex publication_date 2018/12/05 · arxiv updated 2018/12/06 · openalex created_date 2018/12/11 · openalex updated_date 2026/07/28

Abstract

Fang-Wu\citeFW17 presented a explicit spectral gap for the O-U process on path space over a Riemannian manifold without boundary under the bounded Ricci curvature conditions. In this paper, we will extend these results to the case of the Riemannian manifold with boundary. Moreover, we also derive the similar results for the stochastic heat process.

Citations

• The motion of a random string

Related

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• Remarks on spectral gaps on the Riemannian path space
• Stochastic Heat Equations with Values in a Riemannian Manifold
• Stochastic Heat Equations for infinite strings with Values in a Manifold
• Functional inequalities on path space over a non-compact Riemannian manifold