Full Description
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.
Contents
Jump processes related to the two dimensional dirac equation.- A constructive characterization of radon probability measures on infinite dimensional spaces.- A "Brownian motion" with constant speed.- The semi-martingale approach to the optimal resource allocation in the controlled labour-surplus economy.- A central limit theorem for the laplacian in regions with many small holes.- On dirichlet forms with random data—Recurrence and homogenization.- A nicolai map for supersymmetric quantum mechanics on riemannian manifolds.- Stochastic equations for some Euclidean fields.- Percolation of the two-dimensional ising model.- How do stochastic processes enter into physics?.- Estimates on the difference between succeeding eigenvalues and Lifshitz tails for random Schrödinger operators.- On identification for distributed parameter systems.- Fock space and probability theory.- On a transformation of symmetric markov process and recurrence property.- On absolute continuity of two symmetric diffusion processes.- Collective phenomena in stochastic particle systems.- Boundary problems for stochastic partial differential equations.- Generalized one-sided stable distributions.- Quantum fields, gravitation and thermodynamics.- Self-repellent random walks and polymer measures in two dimensions.- On the uniquness of the markovian self-adjoint extension.- Representations of the group of equivariant loops in SU(N).- Proof of an algebraic central limit theorem by moment generating functions.- Averaging and fluctuations of certain stochastic equations.- Semimartingale with smooth density — The problem of "nodes".
