ABSTRACT
This research introduces a theoretical framework to establish convergence bounds for continuous-state Markov processes using Ricci flow and optimal transport theory, improving mixing properties and deriving quantitative Wasserstein contraction estimates.
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Key findings
Develops a time-dependent metric evolution to adapt the geometry of the state space.
Generalizes the Bakry-Emery curvature-dimension condition through Ricci flow.
Derives Wasserstein contraction estimates valid for non-reversible, non-gradient processes.
Introduces a coupled system of forward Markov semigroup and backward metric evolution.
Limitations & open questions
Further research needed for practical implementation and specific process applications.