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

Published online by Cambridge University Press:  20 November 2018

J. B. Baillon ,
PH. Clément ,
A. Greven  and
F. Den Hollander
J. B. Baillon
Affiliation:
Institut de Mathématiques et Informatique Université de Lyon I 43 Bd du 11 novembre 1918 F-69622 Villeurbanne Cedex France
PH. Clément
Affiliation:
Faculteit der Technische Wiskunde en Informatica Technische Universiteit DelftMekelweg 4 NL-2600 GA Delft The Netherlands
A. Greven
Affiliation:
Mathematisches Institut Universität Erlangen-NürnbergBismarckstrasse 1-½ D-91054 Erlangen Germany
F. Den Hollander
Affiliation:
Mathematisch Instituut Universiteit Nijmegen Toernooiveld1 NL-6525 ED Nijmegen The Netherlands
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Abstract

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This 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.

Keywords

60K3547H99
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 1 , 01 February 1995 , pp. 3 - 27
Copyright
Copyright © Canadian Mathematical Society 1995

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