Geodesic random walks, diffusion processes, and Brownian motion on Finsler manifolds
Date: 11 May 2023, Thursday
Time: 5pm AEST
Statistics
and Stochastic colloquium (part of the Colloquium Series of the
Department of Mathematics and Statistics) at La Trobe University jointly
organized with the Probability Victoria Seminar.
Contact the organizers: Andriy Olenko a.olenko@latrobe.edu.au, Kostya Borovkov kostya.borovkov@gmail.com
Speaker: Prof Vladimir S. Matveev (Die Friedrich-Schiller-Universität Jena, the Federal Republic of Germany // La Trobe University, the Commonwealth of Australia)
Abstract: We show that geodesic random walks on a
complete Finsler manifold of bounded geometry converge to a diffusion
process which is, up to a drift, the Brownian motion corresponding to a
Riemannian metric. In particular, the generator of the limit process is a
non-degenerate elliptic second-order partial differential operator for
which we give a precise integral formula. If the geodesic random walk is
geometric, that is if the law of increments are constructed by the
Finsler metric by a coordinate-invariant procedure, the Riemannian
metric is then determined by the Finsler metric. Special cases of such
functors F → g_F include
the Binet-Legendre metric and different average metrics and has many
effective applications in Finsler geometry in which in particular
certain mathematicians from the La Trobe University are involved. Also
possible applications in natural and life sciences will be discussed.
Most results are joint with Tianyu Ma and Ilya Pavlyukevich.
Zoom meeting link:
https://unimelb.zoom.us/j/86301899265?pwd=ZmRqWVBDRzM1azlpRjVHWG5HaEZOUT09
(if the above link doesn't work when you click it -- please copy & paste it into the address bar in your browser).
Password: 277885 (just in case)
A
PDF file with the talk slides might become available for downloading
from our seminar Webpage at https://probvic.wordpress.com/pvseminar/
prior to the talk (the above Zoom link is already there).
