ON THE DOUGLAS-KAZAKOV PHASE TRANSITION
ON THE DOUGLAS-KAZAKOV PHASE TRANSITION
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关于道格拉斯-卡扎科夫相变
DOI：
10.1051/proc/201551006
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Mylene Maida
中科院分区：
文献类型：
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作者：
Thierry Lévy;Mylene Maida
我们给出了Douglas和Kazakov于1993年在二维规范理论中发现的相变发生的严格证明。这种相变可以用大尺度酉群上的布朗桥来表示。我们解释了如何通过考虑酉布朗桥的特征值的渐近行为来理解它，以及如何通过对酉群的傅里叶分析在技术上接近它。此外，我们提出了一些或多或少的经典方法来解决某些最小化问题，这些问题在相变研究中起着重要作用，更广泛地说，在所谓的“离散库仑气体”中起着重要作用。
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 in large dimension. 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 and more generally in what can be called 'discrete Coulomb gases'.