Asymptotic sine laws arising from alternating random permutations and sequences
Gordon D. Simons, Yi‐Ching Yao · Random Structures and Algorithms · 1996
In the last century, Désiré André obtained many remarkable properties of the numbers of alternating permutations, linking them to trigonometric functions among other things. By considering the probability that a random permutation is alternating and that a random sequence (from a uniform distribution) is alternating, and by conditioning on the first element of the sequence, his results are extended and illuminated. In particular, several “asymptotic sine laws” are obtained, some with exponential rates of convergence. © 1996 John Wiley & Sons, Inc.