2 p.m. - 3 p.m. Location: FN 1.202
Mathematics and Electrical & Computer Engineering,
University of Texas at Austin
Dynamics on Random Networks
The talk will be focused on dynamics on discrete random structures.
We will first consider compatible dynamics on the points of a stationary point process, namely “rules to navigate from point to point" which are preserved by translations. Each such dynamics defines a random graph on the points of the process. The connected components of this graph can be split into a collection of foils, which are the analogue of the stable manifold of the dynamics.
We will give a general classification of such dynamics in terms of the cardinality of the foils of these connected components. There are three types: F/F (finitely many finite foils), I/F (infinitely many finite foils), and I/I.
We will then consider compatible dynamics on random graphs and random networks (marked graphs), namely “rules to navigate from node to node" which are preserved by graph or network isomorphisms. We will show that this classification also holds for all unimodular random graphs and networks. We will complement this by analytical results on the relative intensities of the foils.
These results will be illustrated by concrete examples of navigation rules, both on point processes and on random networks.
Joint work with M.-O. Haji-Mirsadeghi, Department of Mathematics, Sharif University, and A. Khezeli, Department of Mathematics, UT Austin.
Sponsored by the Department of Mathematical Sciences