Improved bounds for the mixing time of the random-to-random shuffle
Chuan Qin, Ben Morris · Electronic Communications in Probability · 2017
We prove an upper bound of $1.5321 n \log n$ for the mixing time of the random-to-random insertion shuffle, improving on the best known upper bound of $2 n \log n$. Our proof is based on the analysis of a non-Markovian coupling.