Nous considérons la mesure uniforme sur l’ensemble des configurations de Gelfand–Tsetlin de profondeur
Nous prouvons que le noyau de corrélation des particules dans le voisinage d’un « point typique du bord » converge vers le noyau de Airy étendu. A cette fin, nous trouvons dans un premier temps un dimensionnement adéquat pour la fluctuation des particules. Nous donnons une paramétrisation explicite du noyau asymptotique, définissons une courbe non-asymptotique analogue (et son équivalent en dimension
We impose the uniform probability measure on the set of all discrete Gelfand–Tsetlin patterns of depth
We prove that the correlation kernel of particles in the neighbourhood of “typical edge points” convergences to the extended Airy kernel. To do this, we first find an appropriate scaling for the fluctuations of the particles. We give an explicit parameterisation of the asymptotic edge, define an analogous non-asymptotic edge curve (or finite
Keywords: Random lozenge tilings, Universal edge fluctuations, Steepest descent
Mot clés : Random lozenge tilings, Universal edge fluctuations, Steepest descent
@article{AMBP_2018__25_1_75_0, author = {Duse, Erik and Metcalfe, Anthony}, title = {Universal edge fluctuations of discrete interlaced particle systems}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {75--197}, publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal}, volume = {25}, number = {1}, year = {2018}, doi = {10.5802/ambp.373}, language = {en}, url = {https://www.numdam.org/articles/10.5802/ambp.373/} }
TY - JOUR AU - Duse, Erik AU - Metcalfe, Anthony TI - Universal edge fluctuations of discrete interlaced particle systems JO - Annales mathématiques Blaise Pascal PY - 2018 SP - 75 EP - 197 VL - 25 IS - 1 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - https://www.numdam.org/articles/10.5802/ambp.373/ DO - 10.5802/ambp.373 LA - en ID - AMBP_2018__25_1_75_0 ER -
%0 Journal Article %A Duse, Erik %A Metcalfe, Anthony %T Universal edge fluctuations of discrete interlaced particle systems %J Annales mathématiques Blaise Pascal %D 2018 %P 75-197 %V 25 %N 1 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U https://www.numdam.org/articles/10.5802/ambp.373/ %R 10.5802/ambp.373 %G en %F AMBP_2018__25_1_75_0
Duse, Erik; Metcalfe, Anthony. Universal edge fluctuations of discrete interlaced particle systems. Annales mathématiques Blaise Pascal, Tome 25 (2018) no. 1, pp. 75-197. doi : 10.5802/ambp.373. https://www.numdam.org/articles/10.5802/ambp.373/
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