Events for 10/20/2014 from all calendars

Free Probability Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Wonhee Na, TAMU

Title: Free probability for pairs of faces

Abstract: Recently, Voiculescu introduced Free probability for pairs of faces, a generalization of the notion of free probability to the simultaneous study of left and right operators on the free product space. We define bi-freeness for pairs of faces in a noncommutative probability space and go through several examples of a bi-free family of pairs of faces including left and right creation operators on the full Fock space. We consider universal polynomials in a bi-free system, bi-free cumulants, and the bi-free central limit theorem. For the simplest type of bi-free culmulants, we prove a formula for the partial bi-free R-transform of a two-faced pair. For a system with rank at most 1 commutation, we show that the distribution is completely determined by its two-bands distributions and its coefficient matrix. This talk is based on Voiculescu’s two papers: (1) Free probability for pairs of faces 1 and (2) Free probability for pairs of faces 2: 2-variables bi-free partial R-transform and systems with rank ≤1 commutation.