Abstract
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 zerorange, 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 P. A. Ferrari and C. Kipnis' arguments ("Second class particles in the rarefaction fan", Ann. Inst. H. Poincaré, 31, 1995) 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 onesite 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 particleantiparticle pair.
Original language  English 

Pages (fromto)  35353570 
Number of pages  36 
Journal  Annals of Probability 
Volume  45 
Issue number  6A 
Early online date  27 Nov 2017 
DOIs  
Publication status  Published  Nov 2017 
Keywords
 second class particle
 limit distribution
 rarefaction fan
 shock
 hydrodynamic limit
 collision probability
Fingerprint
Dive into the research topics of 'How to initialize a second class particle?'. Together they form a unique fingerprint.Profiles

Professor Marton Balazs
 School of Mathematics  Professor of Probability
 Probability, Analysis and Dynamics
 Probability
Person: Academic , Member