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- W1991520303 abstract "Let G be a compact Lie group. Denote by m the Brownian bridge measure on the loop group Y ≡ {g ϵ C([0, 1]; G): g(0) = g(1) = e }. The finite energy subgroup of Y determines in a natural way a gradient operation for functions on Y. The following logarithmic Sobolev inequality is proven, ∝ f2, log ¦f¦dm ⩽ ∝ {¦gradf(y)¦2 + V(y) f (y)2} dm + ∥f∥2log∥f∥wherein ∥f∥ denotes the L2(m) norm and V is a potential which is quadratic in the associated Lie algebra valued Brownian motion. The inequality is derived by a method of inheritance from the known inequality for the G valued Brownian motion." @default.
- W1991520303 created "2016-06-24" @default.
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- W1991520303 date "1991-12-01" @default.
- W1991520303 modified "2023-09-23" @default.
- W1991520303 title "Logarithmic Sobolev inequalities on loop groups" @default.
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- W1991520303 doi "https://doi.org/10.1016/0022-1236(91)90123-m" @default.
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