For K-symmetric exclusion from a step profile, the rescaled point process of extreme particles converges to a Poisson random measure with intensity proportional to e^{-x} dx.
Stationary fluctuation for the occupation time of the multi-species stirring process
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In this paper, we prove a fluctuation theorem for the occupation time of the multi-species stirring process on a lattice starting from a stationary distribution. Our result shows that the occupation times of different species interact with each other at the level of equilibrium fluctuation. The proof of our result utilizes the resolvent strategy introduced in \cite{Kipnis1987}. A coupling relationship between the multi-species stirring process and an auxiliary process and a graphical representation of the auxiliary process play the key roles in the proof.
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Point process convergence of extremes in $K$-symmetric exclusion
For K-symmetric exclusion from a step profile, the rescaled point process of extreme particles converges to a Poisson random measure with intensity proportional to e^{-x} dx.