The Poisson boundary of Thompson's group $T$ is not the circle

Martín Gilabert Vio, Cosmas Kravaris, Eduardo Silva

Let $\hat{I}¼$ be a nondegenerate probability measure with finite entropy on a countable group $G\le {\mathrm{Homeo}}_{+}(S^1)$ of orientation-preserving homeomorphisms of the circle actin…