Spectral representation of one-dimensional Liouville Brownian motion and Liouville Brownian excursion

Fractal Geometry and Dynamics

31 October 14:00 - 14:50

Xiong Jin - University of Manchester

The one-dimensional Liouville Brownian motion (LBM) under consideration is a generalized linear diffusion process with natural scale function and speed measure m, where m is the boundary Liouville measure on the real line obtained from the Gaussian free field on the half-plane with Neumann boundary condition. In this talk I will present some classical spectral representation of generalized linear diffusions and their excursions in terms of the speed measure m and its spectral measure. As an application the fractal dimension of the level sets of one-dimensional LBM as well as several probabilistic asymptotic behaviours of LBM are deduced.
Kenneth J. Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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