On the Attracting Orbit of a Non-Linear Transformation Arising From Renormalization Of Hierarchically Interacting Diffusions Part I: The Compact Case

Abstract

AbstractThis paper analyzes the n-fold composition of a certain non-linear integral operator acting on a class of functions on [0,1 ]. The attracting orbit is identified and various properties of convergence to this orbit are derived. The results imply that the space-time scaling limit of a certain infinite system of interacting diffusions has universal behavior independent of model parameters.