Matricial approximations of higher dimensional master fields

Nicolas Gilliers (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

We study matricial approximations of master fields constructed in [6]. These approximations (in non-commutative distribution) are obtained by extracting blocks of a Brownian unitary diffusion (with entries in R, C or K) and letting the dimension of these blocks to tend to infinity. We divide our study into two parts: in the first one, we extract square blocks while in the second one we allow rectangular blocks. In both cases, free probability theory appears as the natural framework in which the limiting distributions are most accurately described.

Domaines: Mathématiques [math]; Physique [physics]

Nicolas Gilliers. Matricial approximations of higher dimensional master fields. 2019. ⟨hal-02113269⟩