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We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their random-cluster representations. More precisely, we prove that
Hugo Duminil-Copin 1 ; Aran Raoufi 1 ; Vincent Tassion 2
@article{10_4007_annals_2019_189_1_2,
author = {Hugo Duminil-Copin and Aran Raoufi and Vincent Tassion},
title = {Sharp phase transition for the random-cluster and {Potts} models via decision trees},
journal = {Annals of mathematics},
pages = {75--99},
publisher = {mathdoc},
volume = {189},
number = {1},
year = {2019},
doi = {10.4007/annals.2019.189.1.2},
mrnumber = {3898174},
zbl = {07003145},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.1.2/}
}
TY - JOUR AU - Hugo Duminil-Copin AU - Aran Raoufi AU - Vincent Tassion TI - Sharp phase transition for the random-cluster and Potts models via decision trees JO - Annals of mathematics PY - 2019 SP - 75 EP - 99 VL - 189 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.1.2/ DO - 10.4007/annals.2019.189.1.2 LA - en ID - 10_4007_annals_2019_189_1_2 ER -
%0 Journal Article %A Hugo Duminil-Copin %A Aran Raoufi %A Vincent Tassion %T Sharp phase transition for the random-cluster and Potts models via decision trees %J Annals of mathematics %D 2019 %P 75-99 %V 189 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.1.2/ %R 10.4007/annals.2019.189.1.2 %G en %F 10_4007_annals_2019_189_1_2
Hugo Duminil-Copin; Aran Raoufi; Vincent Tassion. Sharp phase transition for the random-cluster and Potts models via decision trees. Annals of mathematics, Tome 189 (2019) no. 1, pp. 75-99. doi: 10.4007/annals.2019.189.1.2
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