The ideas and principles of stochastic analysis have managed to penetrate into various fields of pure and applied mathematics in the last 15 years; it is particularly true for mathematical physics. This volume provides a wide range of applications of stochastic analysis in fields as varied as statistical mechanics, hydrodynamics, Yang–Mills theory and spin-glass theory.

The proper concept of stochastic dynamics relevant to each type of application is described in detail here. Altogether, these approaches illustrate the reasons why their dissemination in other fields is likely to accelerate in the years to come.

Contents:

• Stochastic Parallel Transport on the d-Dimensional Torus (A B Cruzeiro & P Malliavin)
• Riemannian Geometry of Diff(S¹)/S¹ Revisited (M Gordina)
• Ergodic Theory of SDE's with Degenerate Noise (A Kupiainen)
• Dynkin’s Isomorphism without Symmetry (Y Le Jan)
• Large Deviations for the Two-Dimensional Yang–Mills Measure (T Lévy)
• Laplace Operator in Networks of Thin Fibers: Spectrum Near the Threshold (S Molchanov & B Vainberg)
• Adiabatic Limits and Quantum Decoherence (R Rebolledo & D Spehner)
• Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects (A N Sengupta)
• Near Extinction of Solution Caused by Strong Absorption on a Fine-Grained Set (V V Yurinsky & A L Piatnitski)