Limit shapes of evacuation and jeu de taquin paths in random square tableaux

Abstract

We consider large random square Young tableaux and look for typical (in the sense of probability) jeu de taquin paths and evacuation paths in the asymptotic setting. We show that the probability distribution of such paths converges to a random meridian connecting the opposite corners of the square.Comment: 12 pages. Extended abstract of FPSAC 2020 conference. A full version of this extended abstract will be available soon as a separate pape