6533b830fe1ef96bd12965eb

RESEARCH PRODUCT

Transportation cost inequalities on path and loop groups

Jinghai ShaoJinghai ShaoShizan FangShizan Fang

subject

Discrete mathematicsPath (topology)Adjoint representationLie groupGirsanov theoremSpace (mathematics)Action (physics)Heat measuresLoop groupsLoop (topology)Loop groupLie algebraWasserstein distanceAnalysisMathematicsH-distance

description

AbstractLet G be a connected Lie group with the Lie algebra G. The action of Cameron–Martin space H(G) on the path space Pe(G) introduced by L. Gross (Illinois J. Math. 36 (1992) 447) is free. Using this fact, we define the H-distance on Pe(G), which enables us to establish a transportation cost inequality on Pe(G). This method will be generalized to the path space over the loop group Le(G), so that we obtain a transportation cost inequality for heat measures on Le(G).

yearjournalcountryeditionlanguage
2005-01-01Journal of Functional Analysis
10.1016/j.jfa.2004.02.002http://dx.doi.org/10.1016/j.jfa.2004.02.002