HEAT KERNEL MEASURE ON LOOP AND PATH GROUPS

DOI10.1142/S0219025708003099zbMath1154.58019OpenAlexW1996935890MaRDI QIDQ3519915

Bruce K. Driver, Matthew Cecil

Publication date: 19 August 2008

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025708003099

zbMATH Keywords

path spaceheat kernel measureloop spacenon-compact Lie group

Mathematics Subject Classification ID

Brownian motion (60J65) Diffusion processes and stochastic analysis on manifolds (58J65) Group structures and generalizations on infinite-dimensional manifolds (58B25) Manifolds of mappings (58D15)

Related Items (4)

Construction of diffusions on current groups ⋮ The Taylor map on complex path groups ⋮ Dimension-independent estimates for heat operators and harmonic functions ⋮ The Ricci curvature of finite dimensional approximations to loop and path groups

Cites Work

• Unnamed Item
• Integration on loop groups. I: Quasi invariant measures
• Brownian motion and the heat semigroup on the path space of a compact Lie group
• Integration by parts and quasi-invariance for heat kernel measures on loop groups
• Integration by parts for heat measures over loop groups
• Canonical Brownian motion on the diffeomorphism group of the circle
• Modulus of continuity of the canonic Brownian motion ``on the group of diffeomorphisms of the circle
• Convergence of finite dimensional distributions of heat kernel measures on loop groups
• Twisted sheets
• Logarithmic Sobolev inequalities for pinned loop groups
• Uniqueness of ground states for Schrödinger operators over loop groups
• The canonic diffusion above the diffeomorphism group of the circle

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