Mean-field approximation for spacing distribution functions in classical systems

Mean-field approximation for spacing distribution functions in classical systems.

We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set of Langevin equations, which are decoupled by u...

Mean-field Approximation of Quantum Systems and Classical Limit

If the two-body interaction φ is sufficiently smooth, the behavior of the system for large N is well understood (Seee for instance Ref.s [1],[2],[3]). Namely, if the initial positions and velocities of the particles are independently and identically distributed according to the probability density f = f(x, v), in the limit N → ∞ each particle is distributed at time t according to the distributi...

Combination of Approximation and Simulation Approaches for Distribution Functions in Stochastic Networks

This paper deals with the fundamental problem of estimating the distribution function (df) of the duration of the longest path in the stochastic activity network such as PERT network. First a technique is introduced to reduce variance in Conditional Monte Carlo Sampling (CMCS). Second, based on this technique a new procedure is developed for CMCS. Third, a combined approach of simulation and ap...

Mean Field Approximation for Fields of Experts

Online Mean Field Approximation for Automated Experimentation

In this paper, we propose a semi-supervised online graph labelling method that a↵ords early learning capability. We use mean field approximation for predicting the unknown labels of the vertices of the graph with high accuracy on the standard benchmark datasets. The minimum cut is the energy function of our probabilistic model that encodes the uncertainty about the labels of the vertices. Our m...