Search results for "Random systems"
showing 3 items of 3 documents
Models of Dynamical Modelling Under Uncertainty
1986
The objective of this work is to modelize the evolution of a Model-System to be adapted to a Random System. This evolution is described by means of the change of a probabilistic function, through deterministic rules and in function of the random responses of the modelized System. This probabilistic function can describe the relative weight of distinct submodels (deterministic or random Systems, with constant or variable stimulus), or the stimulus-response relation in the Model-System (Adaptative Random System). We conclude that the Adaptative Random Model permits a more precise, simple and economical modelling.
Synchronization and fluctuations for interacting stochastic systems with individual and collective reinforcement
2020
The Pólya urn is the paradigmatic example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose a.s. time-limit is not random anymore. In this work, in the stream of previous recent works, we introduce a new family of (finite) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one componentwise, one collective) are tuned through (possibly) different rates n −γ. In the case the reinforcement rates are like n −1 , these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead …
Anderson localization problem: An exact solution for 2-D anisotropic systems
2007
Our previous results [J.Phys.: Condens. Matter 14 (2002) 13777] dealing with the analytical solution of the two-dimensional (2-D) Anderson localization problem due to disorder is generalized for anisotropic systems (two different hopping matrix elements in transverse directions). We discuss the mathematical nature of the metal-insulator phase transition which occurs in the 2-D case, in contrast to the 1-D case, where such a phase transition does not occur. In anisotropic systems two localization lengths arise instead of one length only.