Title: Non-commutative Brownian Motion and a New Class of Topological Algebras

Abstract: We study a family of free stochastic processes whose covariance kernels K may be derived as a transform of a tempered measure σ. These processes arise, for example, in consideration non-commutative analysis involving free probability. Hence our use of semi-circle distributions, as opposed to Gaussians. In this setting we find an orthonormal bases in the corresponding non-commutative L2 of sample-space. We define a stochastic integral for our family of free processes.

Joint work with Palle Jorgensen and Guy Salomon.