Interacting Particle Systems and Riemannian Geometry
J. Junné (TU Delft - Electrical Engineering, Mathematics and Computer Science)
F.H.J. Redig – Promotor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
R. Versendaal – Copromotor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
This thesis is concerned with the broad question:
How is the emergence of deterministic macroscopic laws from random microscopic dynamics influenced by the geometry of the underlying space?
The rigorous derivation of macroscopic equations from microscopic models is a central theme of mathematical physics. In the probabilistic setting, interacting particle systems provide tractable microscopic models made of many particles evolving according to stochastic rules. Under suitable scaling limits, the empirical conserved quantities of these systems are expected to converge to deterministic solutions of partial differential equations. Such results are called hydrodynamic limits....