Stochastic master fields

Stochastic Master Fields

We treat the stochastic equation for large N master fields proposed by Greensite and Halpern using a construction of master fields modelled after work of Voiculescu, and show that it contains the same information as the usual factorized Schwinger-Dyson equations.

Non–commutative (quantum) Probability, Master Fields and Stochastic Bosonization

In this report we discuss some results of non–commutative (quantum) probability theory relating the various notions of statistical independence and the associated quantum central limit theorems to different aspects of mathematics and physics including: q–deformed and free central limit theorems; the description of the master (i.e. central limit) field in matrix models along the recent Singer su...

Master Fields, Drift and Dispersion in the Stochastic Limit of Quantum Theory

This work is a detailed study of the convergence of the rescaled creation and annihilation densities, which lead to the master fields, and the form of the drift in the stochastic limit of quantum theory. The approach, based on the distributional theory of Fourier transforms, dispenses with the “analytical condition” and other restrictions usually considered and also establishes the dependence o...

Master-equation approach to stochastic neurodynamics.

A Master equation approach to the stochastic neurodynamics proposed by Cowan[ in Advances in Neural Information Processing Systems 3, edited by R.P. Lippman, J.E. Moody, and D.S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p.62] is investigated in this paper. We deal with a model neural network which is composed of two-state neurons obeying elementary stochastic transition rates. We show that...

Stochastic Hybrid System for Chemical Master Equation