Limit Fluctuations of Stationary Measure of Totally Asymmetric Simple Exclusion Process with Open Boundaries on the Coexistence Line

We describe limit fluctuations of the height function for the open TASEP on the coexistence line under the stationary measure. It is known that the height function satisfies a law of large numbers as the number of sites n goes to infinity which at the coexistence line is exotic in the sense that the first-order limit is random. Here, we study the functional central limit theorem: we show that with a random centering and normalized by \(\sqrt{n}\), the second-order limit of the height functions is a (random) mixture of two independent Brownian motions.