Cutoff for Kac's Walk on the Sphere
Statement
The discrete-time Kac walk on started from a coordinate vector exhibits total variation cutoff at , where is set by the speed of the leftmost particle in a branching random walk. The cutoff is therefore not at the conjectured .
Context
the conjectured cutoff location of 2n log n is wrong
Kac's walk is a standard model in the mixing-time literature and its cutoff location had a specific conjectured value that this determines and refutes.
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the conjectured cutoff location of 2n log n is wrong
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