Stochastics Seminar

Speaker: Dr. Jerzy Szulga

Title: Algebraic structures induced by random chaos operators

Abstract: The term "random chaos" refers to a highly organized and heavily investigated system of functionals of Brownian motion. In the 1980s K. R. Parthasarathy introduced certain important operators, originated in quantum probability, known as "creation," "annihilation," and "conservation" operators.  In the 1990s P-A. Meyer adopted these quantum concepts to the framework of "discrete random chaos," which in analytic terms refers to Walsh series and discrete Fourier analysis.

The algebras spanned by these three basic operators yield simple yet quite sophisticated structures that break the limits of typical probabilistic endeavors and enter areas usually governed by coding theory, theory of finite fields (especially of characteristic 2), tensor products, Clifford algebras, etc.

The seminar talk is a continuation of my previous presentations on the same topic, now enriched by new developments and results, obtained recently.