Second class particles in exclusion processes
and their connection with increasing sequence models

 
 

A second-class particle in an exclusion-type particle system is a particle with lower priority than the regular particles.  It is the microscopic analogue of the shocks and characteristics of the macroscopic p.d.e. of the system.  Through a variational coupling representation of the exclusion process, a second class particle can also be represented by a variational formula that involves a model of increasing sequences.  From this representation one can derive laws of large numbers and bounds on the fluctuations and large deviations of a second class particle.  As a corollary of the large deviation estimate one gets variance bounds for the occupation time of a site in equilibrium asymmetric exclusion.