Probabilistic Operator Algebra Seminar: An introduction to Boolean independence

Seminar | October 16 | 3:45-5:45 p.m. | 748 Evans Hall

 Jorge Garza Vargas, UC Berkeley

 Department of Mathematics

With the introduction of free independence by D.V. Voiculescu, it became clear that in the framework of non-commutative probability there are other notions of independence than that of classical independence. The Boolean convolution between measures was formally introduced by Speicher and R. Woroudi in 1993, although it had previously appeared in the literature in different contexts, for example, as partial cumulants in stochastic differential equations. Later, in 2006, H. Bercovici provided the product for Hilbert spaces that, in the context of operator algebras, corresponds to the Boolean convolution between measures. In this talk we will survey the basics of Boolean probability, scenarios in which it appears naturally, together with some results that show the similarities and differences it has with the classical theory of probability.