Geodesic
Second class particles and limit shapes of evacuation and sliding paths for random tableaux.
Documenta mathematica, Tome 27 (2022), pp. 2183-2273

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We investigate two closely related setups. In the first one we consider a TASEP-style system of particles with specified initial and final configurations. The probability of each history of the system is assumed to be equal. We show that the rescaled trajectory of the second class particle converges (as the size of the system tends to infinity) to a random arc of an ellipse.
DOI : 10.4171/dm/x28
Classification : 05E10, 60C05, 60K35, 82C22
Mots-clés : second class particles, interacting particle systems, TASEP, random Young tableaux, limit shape, jeu de taquin, promotion, Schützenberger's evacuation, square Young tableaux 
Łukasz Maślanka; Piotr Śniady. Second class particles and limit shapes of evacuation and sliding paths for random tableaux.. Documenta mathematica, Tome 27 (2022), pp. 2183-2273. doi: 10.4171/dm/x28
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     title = {Second class particles and limit shapes of evacuation and sliding paths for random tableaux.},
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     pages = {2183--2273},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x28},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x28/}
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