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math.PR2026
A subquadratic upper bound for the mixing time of the Thorp shuffle
Yunjiang Jiang
Let . We prove that the worst-start total-variation mixing time of the full labelled Thorp shuffle satisfies, for every fixed , \[ t_{\mathrm{mix}}(\varepsi…
math.PR2026
Cutoff for the Overhand Shuffle
Yunjiang Jiang
We study the overhand shuffle with a fixed cut probability . In the packet-reversal convention, each gap is cut independently with probability , and each resulting pa…
math.PR2026
Resolvent characteristics and quadratic mixing of Kac's walk on
Yunjiang Jiang
We study the coordinate-plane Kac walk on with independent uniform rotation angles. For the unnormalized Hilbert-Schmidt Riemannian distance, we prove that the Was…