Stochastic Processes - Mathematics and Physics II -

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Résumé :
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.

Sommaire:
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 Schr?dinger 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.