Conservative interacting particles system with anomalous rate of ergodicity
Probability
2015-05-20 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We analyze certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore, we show that convergence rate to equilibrium is exponential. This result is of interest because it presents counterexample to the standard assumption of physicists that conservative system implies polynomial rate of convergence.
Cite
@article{arxiv.1012.0582,
title = {Conservative interacting particles system with anomalous rate of ergodicity},
author = {Zdzislaw Brzeźniak and Franco Flandoli and Misha Neklyudov and Boguslaw Zegarliński},
journal= {arXiv preprint arXiv:1012.0582},
year = {2015}
}
Comments
16 pages; In the previous version there was a mistake in the proof of uniqueness of weak Leray solution. Uniqueness had been claimed in a space of solutions which was too large (see remark 2.6 for more details). Now the mistake is corrected by introducing a new class of moderate solutions (see definition 2.10) where we have both existence and uniqueness