Evolution of Concentration Under Lattice Spin-Flip Dynamics-Reference-Cited by-同舟云学术

Evolution of Concentration Under Lattice Spin-Flip Dynamics

Published:2021-06-25 Issue:1 Volume:184 Page:
ISSN:0022-4715
Container-title:Journal of Statistical Physics
language:en
Short-container-title:J Stat Phys

Author:

Chazottes Jean-René,Collet Pierre,Redig Frank

Abstract

AbstractWe consider spin-flip dynamics of Ising lattice spin systems and study the time evolution of concentration inequalities. For “weakly interacting” dynamics we show that the Gaussian concentration bound is conserved in the course of time and it is satisfied by the unique stationary Gibbs measure. Next we show that, for a general class of translation-invariant spin-flip dynamics, it is impossible to evolve in finite time from a low-temperature Gibbs state towards a measure satisfying the Gaussian concentration bound. Finally, we consider the time evolution of the weaker uniform variance bound, and show that this bound is conserved under a general class of spin-flip dynamics.

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://link.springer.com/content/pdf/10.1007/s10955-021-02796-0.pdf

Reference13 articles.

1. Boucheron, S., Lugosi, G., Massart, P.: Concentration Inequalities. A Nonasymptotic Theory of Independence. Oxford University Press, Oxford (2013)

2. Chazottes, J.-R., Collet, P., Redig, F.: On concentration inequalities and their applications for Gibbs measures in lattice systems. J. Stat. Phys. 169(3), 504–546 (2017)

3. Chazottes, J.-R., Collet, P., Redig, F.: Coupling, concentration inequalities, and stochastic dynamics. J. Math. Phys. 49, no. 12 (2008)

4. Chazottes, J.-R., Collet, P., Redig, F.: Evolution of Gaussian Concentration, preprint arXiv:1903.07915

5. Chazottes, J.-R., Collet, P., Külske, C., Redig, F.: Concentration inequalities for random fields via coupling. Probab. Theory Relat. Fields 137(1–2), 201–225 (2007)