2025/04/10 by Arfaee, Samira, Nestoridi, Evita · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2504.07918
We consider a family of card shuffles of n cards, where the allowed moves involve transpositions corresponding to the Jucys--Murphy elements of \Sm\m ≤ n. We diagonalize the transition matrix of these shuffles. As a special case, we consider the k-star transpositions shuffle, a natural interpolation between random transpositions and star transpositions. We proved that the k-star transpositions shuffle exhibits total variation cutoff at time (2n-(k+1))/(2(n-1))nlog n with a window of (2n-(k+1))/(2(n-1))n. Furthermore, we prove that for the case where k/n → 0 or 1, this shuffle has the same limit profile as random transpositions, which has been fully determined by Teyssier.