2015/03/02 by Thierry Lévy, Lévy, Thierry, Mylène Maïda +2 · 2 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR
paper · pdf · doi:10.48550/arxiv.1503.00502
arxiv created 2015/03/02 · openalex publication_date 2015/03/02 · arxiv updated 2015/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.