We compute that the growth of the occupation-time variance at the origin up to time t in dimension d = 2 with respect to asymmetric simple exclusion in equilibrium with density ρ = 1/2 is in a certain sense at least tlog (log t) for general rates, and at least t(log t) 1/2 for rates which are asymmetric only in the direction of one of the axes. These estimates give a complement to bounds in the literature when d = 1, and are consistent with an important conjecture with respect to the transition function and variance of "second-class" particles.
- Second-class particle
- Secondary 60F05
- Simple exclusion AMS (2000) subject classifications: Primary 60K35
- Variance of occupation times
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics