2013/03/10 by Ümi̇t Işlak, Umit Islak, Islak, Umit · 1 citation
Computer Science · Mathematics · #Algorithms and Data Compression #Bayesian Methods and Mixture Models #Stochastic processes and statistical mechanics #math.CO
paper · pdf · doi:10.48550/arxiv.1303.2387
13 pages
arxiv created 2013/03/10 · arxiv updated 2013/03/12
This paper studies statistics of riffle shuffles by relating them to random word statistics with the use of inverse shuffles. Asymptotic normality of the number of descents and inversions in riffle shuffles with convergence rates of order 1/√(n) in the Kolmogorov distance are proven. Results are also given about the lengths of the longest alternating subsequences of random permutations resulting from riffle shuffles. A sketch of how the theory of multisets can be useful for statistics of a variation of top m to random shuffles is presented.