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1. Superdiffusivity of occupation-time variance in 2-dimensional asymmetric processes with density 1/2 is ‘second-class’ particles.

   What is 2-dimensional asymmetric exclusion processes?

   • The two-species asymmetric diffusive process [23] is modeled on the two-dimensional lattice with two types of particles.
   • The first set of particles is allowed to move only along the positive x direction (to the right) and second set of particles moves to the positive y direction.

   • We compute that the growth of the origin occupation-time variance up to time t in dimension d=2 with respect to asymmetric simple exclusion in equilibrium with density 1/2 is in a certain sense at least t(log(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 are consistent with conjectures with respect to the transition function and variance of ‘second-class’ particles.

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