Phénomène de cutoff pour certaines marches aléatoires sur le groupe symétrique
The main purpose of this paper is to exhibit the cutoff phenomenon, studied by Aldous and Diaconis [AD]. Let denote a transition kernel after k steps and π be a stationary measure. We have to find a critical value for which the total variation norm between and π stays very close to 1 for , and falls rapidly to a value close to 0 for with a fall-off phase much shorter than . According to the work of Diaconis and Shahshahani [DS], one can naturally conjecture, for a conjugacy class with...