Multifractal Analysis in Infinite Dimension of the Wiener Measure

Mathphys Analysis Seminar

This talk presents joint work with Ai Hua Fan in which we propose a multifractal formalism for measures defined on metric spaces of infinite dimension. This formalism is expressed in terms of scales rather than dimensions. With an appropriate choice of scale, called the order, we obtain what appears to be the first example of a multifractal object of infinite dimension: standard Brownian motion. The associated multifractal spectrum is derived from the study of small deviations centered around atypical trajectories, classified according to their regularity, such as trajectories typical of fractional Brownian motions.