Fluctuation limits for two-dimensional mean-zero asymmetric exclusion

Determine the properly scaled fluctuation limit for centered occupation-time functionals in two-dimensional mean-zero asymmetric exclusion and related particle systems started from an invariant measure.

Background

The notes distinguish mean-zero asymmetric systems from symmetric and nonzero-drift asymmetric systems. They report that in one dimension, properly scaled occupation variables can converge to fractional Brownian motion, while higher-dimensional cases involve different variance and fluctuation behavior.

For two-dimensional mean-zero asymmetric systems, the fluctuation limit of properly scaled centered occupation functionals remains unknown. The problem concerns identifying both the correct scaling and the limiting process.