On the Attracting Orbit of a Nonlinear Transformation Arising from Renormalization of Hierarchically Interacting Diffusions
✍ Scribed by J.-B. Baillon; Ph. Clément; A. Greven; F. den Hollander
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 613 KB
- Volume
- 146
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
This paper analyzes the n-fold composition of a non-linear integral operator acting on a class of functions on [0, ). Attracting orbits and attracting fixed points are identified. Various results of convergence to these orbits and to these fixed points are derived. The proofs are based on order-preserving properties and comparison techniques. A key role is played by the eigenfunctions of the operator, which are used as comparison objects. The results imply that the space-time scaling limit of an infinite system of interacting diffusions has universal behavior independent of model parameters. The paper can be read independently of Part I.