Abstract
We consider a class of probability distributions on the six-vertex model, which originate from the higher spin vertex models in (Selecta Math. (N.S.) 24 (2018) 751–874) and have previously been investigated in (Int. Math. Res. Not. 2020 (2020) 1794–1881). For these random six-vertex models we show that the asymptotic behavior near their base is asymptotically described by the GUE-corners process.
Nous considérons une classe de distributions de probabilités sur le modèle à six sommets, qui provient du modèle à six-sommets aux plus hauts spins, cf (Selecta Math. (N.S.) 24 (2018) 751–874), et qui a été étudiée précédemment dans (Int. Math. Res. Not. 2020 (2020) 1794–1881). Pour ces modèles à six sommets, nous montrons que le comportement asymptotique près de la base est décrit par le processus GUE en coins.
Acknowledgements
The authors would like to thank Ivan Corwin and Ioannis Karatzas for many helpful conversations. M. R. is partially supported by the NSF grant DMS: 1664650. E. D. is partially supported by the Minerva Foundation Fellowship.
Citation
Evgeni Dimitrov. Mark Rychnovsky. "GUE corners process in boundary-weighed six-vertex models." Ann. Inst. H. Poincaré Probab. Statist. 58 (1) 188 - 219, February 2022. https://doi.org/10.1214/21-AIHP1162
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