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math.PR2026
Total variation cutoff for Kac's walk on the sphere
Vishesh Jain, Clayton Mizgerd
The paper proves that the discrete-time Kac walk on the (n‑1)-dimensional sphere, started from a coordinate vector, exhibits a total‑variation cutoff at time C_{BRW}·n·log n (with…
math.PR2024
Hitting time mixing for the random transposition walk
Vishesh Jain, Mehtaab Sawhney
Consider shuffling a deck of cards, labeled through , as follows: at each time step, pick one card uniformly with your right hand and another card, independently and uni…