Responsable : Geoffrey Powell
Brownian motion is an elementary process studied in probability theory. At the same time many interesting objects in modern probability theory and mathematical physics can be regarded as functionals of Brownian motions. In this talk I will pick up the Schramm-Loewner evolution (SLE) from the study of critical phenomena, random fractal geometry, and the conformal field theory, and the Dyson model from the random matrix theory. I introduce a one-parameter family of stochastic processes called the Bessel processes, in which the parameter is the dimensionality of space D generalized to be continuous and positive real-valued. I discuss the parenthood of the Brownian motion to the Bessel processes and that of the Bessel processes to SLE/Dyson model. I will also give a comment on the Kardar-Parisi-Zhang (KPZ) equation from these points of view.