Large time asymptotics for the fluctuation SPDE in the Kuramoto synchronization model
Probability
2013-12-09 v2 Disordered Systems and Neural Networks
Analysis of PDEs
Adaptation and Self-Organizing Systems
Abstract
We investigate the long-time asymptotics of the fluctuation SPDE in the Kuramoto synchronization model. We establish the linear behavior for large time and weak disorder of the quenched limit fluctuations of the empirical measure of the particles around its McKean-Vlasov limit. This is carried out through a spectral analysis of the underlying unbounded evolution operator, using arguments of perturbation of self-adjoint operators and analytic semigroups. We state in particular a Jordan decomposition of the evolution operator which is the key point in order to show that the fluctuations of the disordered Kuramoto model are not self-averaging.
Keywords
Cite
@article{arxiv.1204.2176,
title = {Large time asymptotics for the fluctuation SPDE in the Kuramoto synchronization model},
author = {Eric Lucon},
journal= {arXiv preprint arXiv:1204.2176},
year = {2013}
}
Comments
34 pages, 5 figures; V2: introduction simplified, references added and typos corrected