Ivan Z. Feng

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math.PR2026

Cutoff profiles for colored top-m-to-random shuffles with growing block size

Ivan Z. Feng

We study the $p$ -colored top- $m$ -to-random shuffle on $C_{p} ≀ S_{n}$ when the block size $m = m_{n}$ grows with $n$ . Let $E_{k_{n}}^{(m_{n})}$ be the number of labels never touched after $k_…

math.PR2026

Explicit cutoff profiles for colored top- $m$ -to-random shuffles

Ivan Z. Feng

We study $p$ -colored top- $m$ -to-random on the wreath product $G_{n, p} = C_{p} ≀ S_{n}$ , with $m$ fixed. Using the Nakano-Sadahiro-Sakurai basis elements $B_{m}$ , we obtain exact nested-se…

math.PR2026

The dual Burnside process

Ivan Z. Feng

The Burnside process is a classical Markov chain for sampling uniformly from group orbits. We introduce the dual Burnside process, obtained by interchanging the roles of group elem…

math.PR2026

Analysis of a twisted Bose-Einstein Markov chain with applications to sampling Catalan structures

Ivan Z. Feng, J. E. Paguyo

We analyze a twisted Bose-Einstein Markov chain on $[k]^{n}$ arising from the Diaconis-Zhong twisted Burnside process. We derive explicit formulas for the transition kernel and stati…

Cutoff profiles for colored top-m-to-random shuffles with growing block size

Explicit cutoff profiles for colored top-m-to-random shuffles

The dual Burnside process

Analysis of a twisted Bose-Einstein Markov chain with applications to sampling Catalan structures

Explicit cutoff profiles for colored top- $m$ -to-random shuffles