Given a finite graph G, a vertex of the lamplighter graph over G consists of a zero-one labeling of the vertices of G, along with a marked vertex of G. We find that there is a sharp threshold for the mixing time on the lamplighter graph, at half the cover time of the base graph G in some cases (such as the complete graph) and at the cover time in other cases (such as the 2D discrete torus). We will explain when we expect a sharp threshold for mixing time on a lamplighter graph, and why it is at
half the cover time for some examples and at the cover time in others.

Keywords:

Phase Transitions; computation;reconstruction

Lecture #10878

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