Rick Kun-Hung Hsueh, Department of Pure Mathematics, University of Waterloo
"An analogy between classical and free Brownian motion: A combinatorial approach"
The first part of the talk deals with how plane integer lattice paths can be exploited to calculate moments of random variables of the form A + B, where A, B are linear operators defined on the the full Fock space. In particular, this covers the cases for Gaussian and Wigner semicircle laws which are indispensable parts for classical and free Brownian motion.
The second part focuses on how the structure of the lattice of partition of n-elements can be used to work out an explicit formula in writing the polynomial chaos in terms of the homogeneous chaos. Along the way, we shall define the terms: stochastic integrals and their solution spaces, which are used to make our chaos decomposition results precise.
If time permits, we shall also outline how Möbius inversion formula can be utilized to obtain an expression of homogeneous chaos in terms of polynomial chaos. This last formula allows us to interpret statistical processes driven by free or classical Brownian motion intuitively.
M3 3103