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LCN2 Seminar: Mixing of random walks on dynamic graphs with a fixed degree sequence

Friday 25 November 2022
Snellius room 313

Abstract: While mixing of random walks on static random graphs is now a well-studied topic, much less is known about mixing profiles of random walks on dynamic random graphs. In this talk, I will discuss two results about random walk mixing on dynamic random graphs with a fixed degree sequence.

In the first example, given mild regularity conditions, I will show a simple link between the situation on a static graph and its dynamic counterpart; and that the dynamics generally cause a faster approach to equilibrium. 
In the second example, I will focus on a "fast" random walk on dynamic graphs whose all vertices have degrees equal to two. In this case, the approach to equilibrium is driven by the graph dynamics and there is a peculiar limiting mixing profile with a discontinuity at a random time.

The first part is based on this article and the second part is a work in progress. Joint work with L. Avena, H. Güldaş, R. van der Hofstad and F. den Hollander.

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