HOW TO INITIALIZE A SECOND CLASS PARTICLE?

• 成果类型: Article
• 署名作者: Balazs, Marton; Nagy, Attila Laszlo
• 署名单位: University of Bristol; Budapest University of Technology & Economics
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1143
• 发表日期: 2017
• 页码: 3535-3570
• 关键词: zero-range process; hydrodynamic limit; deposition models; rarefaction fan; competition interfaces; local equilibrium; exclusion process; infinite volume; shocks; systems

摘要

We identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle systems with established hydrodynamic behavior, respectively (including zero-range, misanthrope and many other models). The initial condition is a step profile, which in some classical cases of asymmetric models, gives rise to a rarefaction fan scenario. We also point out a model with nonconcave, nonconvex hydrodynamics, where the rescaled second class particle distribution has both continuous and discrete counterparts. The results follow from a substantial generalization of Ferrari and Kipnis' arguments (Ann. Inst. H. Poincare 31 (1995) 143-154) for the totally asymmetric simple exclusion process. The main novelty is the introduction of a signed coupling measure as initial data, which nevertheless results in a proper probability initial distribution for the site of the second class particle and makes the extension possible. We also reveal in full generality a very interesting invariance property of the one-site marginal distribution of the process underneath the second class particle which in particular proves the intrinsicality of our choice for the initial distribution. Finally, we give a lower estimate on the probability of survival of a second class particle-antiparticle pair.