Transportation cost inequalities on path and loop groups
نویسندگان
چکیده
منابع مشابه
Transportation-Cost Inequalities on Path Space over Manifolds with Boundary
Let L = ∆ + Z for a C vector field Z on a complete Riemannian manifold possibly with a boundary. A number of transportation-cost inequalities on the path space for the (reflecting) L-diffusion process are proved to be equivalent to the curvature condition Ric−∇Z ≥ −K and the convexity of the boundary (if exists). These inequalities are new even for manifolds without boundary, and are partly ext...
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Let L = ∆+Z for a C1 vector field Z on a complete Riemannian manifold possibly with a boundary. By using the uniform distance, a number of transportation-cost inequalities on the path space for the (reflecting) L-diffusion process are proved to be equivalent to the curvature condition Ric−∇Z ≥ −K and the convexity of the boundary (if exists). These inequalities are new even for manifolds withou...
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1.1. Background The existence and properties of Brownian motion on L(K), the pinned loop group of a compact Lie group K, have been studied in a number of papers starting with Refs. 20, 21 and then followed by Refs. 2, 3, 6, 8, 9, 12, 14, 16, 24. (This is only a partial list.) Similar results have been obtained on W(K), the pinned path group, in Ref. 11. Of fundamental importance in these constr...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2005
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2004.02.002