ERGODIC MEASURES AND INFINITE MATRICES OF FINITE RANK

Yanqi Qiu (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

Let $O(\infty)$ and $U(\infty)$ be the inductively compact infinite orthogonal group and infinite unitary group respectively. The classifications of ergodic probability measures with respect to the natural group action of $O(\infty)\times O(m)$ on $\mathrm{Mat}(\mathbb{N}\times m, \mathbb{R})$ and that of $U(\infty)\times U(m)$ on $\mathrm{Mat}(\mathbb{N}\times m, \mathbb{C})$ are due to Olshanski. The original proofs for these results are based on the asymptotic representation theory. In this note, by applying the Vershik-Kerov method, we propose a simple method for obtaining these two classifications, making it accessible to pure probabilists.

Mots clés: and phrases inductively compact groups; ergodic measures; Vershik- Kerov ergodic method; ergodic decomposition

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Yanqi Qiu. ERGODIC MEASURES AND INFINITE MATRICES OF FINITE RANK. 2017. ⟨hal-01483634⟩