Stochastic lie group-valued measures and their relations to stochastic curve integrals, gauge fields and markov cosurfaces.- Existence and sample path properties of the diffusions in Nelson's stochastic mechanics.- Characteristic exponents for stochastic flows.- Electric field and effective dielectric constant in random media with non-linear response.- Remarks on the central limit theorem for weakly dependent random variables.- Time reversal on Wiener space.- Lattice gauge theory; Heuristics and convergence.- The generalized Malliavin calculus based on Brownian sheet and Bismut's expansion for large deviation.- An elementary approach to Brownian motion on manifolds.- The stochastic mechanics of the ground-state of the hydrogen atom.- Nonstandard analysis and perturbations of the laplacian along Brownian paths.- Haussdorf dimension for the statistical equilibrium of stochastics flows.- Stopping problems of symmetric Markov processes and non-linear variational inequalites.- Mean exit times and hitting probabilities of Brownian motion in geodesic balls and tubular neighborhoods.- Rigorous scaling laws for Dyson measures.- Asymptotic freedom: A rigorous approach.- The fermion stochastic calculus I.
Inhaltsverzeichnis
Stochastic lie group-valued measures and their relations to stochastic curve integrals, gauge fields and markov cosurfaces.- Existence and sample path properties of the diffusions in Nelson's stochastic mechanics.- Characteristic exponents for stochastic flows.- Electric field and effective dielectric constant in random media with non-linear response.- Remarks on the central limit theorem for weakly dependent random variables.- Time reversal on Wiener space.- Lattice gauge theory; Heuristics and convergence.- The generalized Malliavin calculus based on Brownian sheet and Bismut's expansion for large deviation.- An elementary approach to Brownian motion on manifolds.- The stochastic mechanics of the ground-state of the hydrogen atom.- Nonstandard analysis and perturbations of the laplacian along Brownian paths.- Haussdorf dimension for the statistical equilibrium of stochastics flows.- Stopping problems of symmetric Markov processes and non-linear variational inequalites.- Mean exit times and hitting probabilities of Brownian motion in geodesic balls and tubular neighborhoods.- Rigorous scaling laws for Dyson measures.- Asymptotic freedom: A rigorous approach.- The fermion stochastic calculus I.
Klappentext
This second BiBoS volume surveys recent developments in the theory of stochastic processes. Particular attention is given to the interaction between mathematics and physics.
Main topics include: statistical mechanics, stochastic mechanics, differential geometry, stochastic proesses, quantummechanics, quantum field theory, probability measures, central limit theorems, stochastic differential equations, Dirichlet forms.
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