On the attracting orbit of a nonlinear transformation arising from renormalization of hierarchically interacting diffusion. Part II: The noncompact case - Baillon, Jean-Bernard; Clément, Philippe P. J. E.; Greven, Andreas; den Hollander, Frank (Journal of Functional Analysis, 1997)
This paper analyzes then-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. © 1997 Academic Pres