Limit fluctuations of stationary measures of totally asymmetric simple exclusion processes with open boundaries on the coexistence line

Włodzimierz Bryc, Joseph Najnudel, Yizao Wang

Published 2024-07-30Version 1

We characterize limit fluctuations of height functions of the totally asymmetric simple exclusion processes with open boundaries at the co-existence line under the stationary measures. The limit behavior of the height functions at the co-existence line was known to be exotic in the sense that the first-order limit theorem (when divided by $n$) has a random limit. Here, we show that with a random centering and then divided by $\sqrt n$, the second-order limit of the height functions is a (random) mixture of two independent Brownian motions.