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Séminaire Lotharingien de Combinatoire, 84B.8 (2020), 12 pp.

# Łukasz Maślanka and Piotr Śniady

# 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.

Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.

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