Abstract
Consider a generalized model of the facilitated exclusion process, which is a one-dimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x + 1 (or x − 1) if the sites x − 1, x − 2 (or x + 1, x + 2) are empty. It is non-gradient and lacks invariant measures of product form. The purpose of this paper is to identify the invariant measures and to show that they satisfy both exponential decay of correlations and equivalence of ensembles. These properties will play a pivotal role in deriving the hydrodynamic limit.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
O Blondel, C Erignoux, M Sasada, M Simon. Hydrodynamic limit for a facilitated exclusion process, Ann Inst Henri Poincaré Probab Stat, 2020, 56(1): 667–714.
P Gonçalves, C Landim, C Toninelli. Hydrodynamic limit for a particle system with degenerate rates, Ann Inst Henri Poincaré Probab Stat, 2009, 45(4): 887–909.
C Kipnis, C Landim. Scaling limits of interacting particle systems, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1999, 320.
Y Lei, Z Su. Hydrodynamic limit for the d-facilitated exclusion process (preprint).
T Liggett. Interacting particle systems. Classics in Mathematics, Springer-Verlag, Berlin, 2005.
A Lukyanov, V Mitkin, T Pryer, P Sirimark, T Theofanous. Capillary transport in paper porous materials at low saturation levels: normal, fast or superfast? Proc R Soc A, 2020, 476: 20200488.
A Lukyanov, M Sushchikh, M Baines, T Theofanous. Superfast nonlinear diffusion: Capillary transport in particulate porous media, Phys Rev Lett, 2012, 109: 214501.
E Miles. Generalized Fibonacci numbers and associated matrices, Amer Math Monthly, 1960, 67: 745–752.
C Stone. On local and ratio limit theorems, Proc Fifth Berkeley Sympos Math Statist and Probability, Vol 2: Contributions to Probability Theory, Part 2, 1967(5.2B): 217–224.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest The authors declare no conflict of interest.
Additional information
Supported in part by the National Natural Science Foundation of China(11731012, 11871425, 12271475) and Fundamental Research Funds for Central Universities grant(2020XZZX002-03).
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the articles Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the articles Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Lei, Yh., Su, Zg. Invariant measures for the strong-facilitated exclusion process. Appl. Math. J. Chin. Univ. 38, 317–337 (2023). https://doi.org/10.1007/s11766-023-4603-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11766-023-4603-1