ON THE DOUGLAS-KAZAKOV PHASE TRANSITION : WEIGHTED POTENTIAL THEORY UNDER CONSTRAINT FOR PROBABILISTS

Abstract : We give a rigorous proof of the fact that a phase transition discovered by Douglas and Kazakov in 1993 in the context of two-dimensional gauge theories occurs. This phase transition can be formulated in terms of the Brownian bridge on the unitary group U(N) when N tends to infinity. We explain how it can be understood by considering the asymptotic behaviour of the eigenvalues of the unitary Brownian bridge, and how it can be technically approached by means of Fourier analysis on the unitary group. Moreover, we advertise some more or less classical methods for solving certain minimisation problems which play a fundamental role in the study of the phase transition.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01121657
Contributeur : Mylène Maïda <>
Soumis le : lundi 2 mars 2015 - 13:19:30
Dernière modification le : vendredi 28 avril 2017 - 01:02:46
Document(s) archivé(s) le : mardi 2 juin 2015 - 09:36:20

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  • HAL Id : hal-01121657, version 1
  • ARXIV : 1503.00502

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Thierry Lévy, Mylene Maida. ON THE DOUGLAS-KAZAKOV PHASE TRANSITION : WEIGHTED POTENTIAL THEORY UNDER CONSTRAINT FOR PROBABILISTS. 2015. <hal-01121657>

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