Intermediate scaling regimes for kinetic transport

Lead Research Organisation: University of Bristol
Department Name: Mathematics


The project seeks to establish diffusive and superdiffusive limit theorems for particle
transport in the Lorentz gas in the case of intermediate scaling limits for both random
and periodic scatterer configurations.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509619/1 01/10/2016 30/09/2021
1793795 Studentship EP/N509619/1 01/10/2016 31/03/2020 Christopher Lutsko
Description We have made significant progress in our understanding of diffusion in particle systems. Specifically the Lorentz gas. In so doing, we developed a new method using probabilistic coupling to introduce probabilistic techniques into the study of particle systems.

Moreover, in a second project we have fully characterised the local statistics for orbits of thin groups. In doing so we extended methods from classical homogeneous dynamics to the thin group setting.
Exploitation Route It would be very interesting to apply the probabilistic methods developed by myself and Balint Toth to more systems. It is also possible that these methods could be extended to longer times and stronger results could be achieved for the classical systems we study.

In addition the study of thin groups is a hot topic in modern mathematics. Applying homogeneous dynamics methods to that setting is an interesting prospect. This could further our understanding of fractals.
Sectors Other