Extreme value statistics of 2D Gaussian free field: effect of finite domains

Extreme value statistics of 2D Gaussian free field: effect of finite domains
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二维高斯自由场的极值统计：有限域的影响

DOI：
10.1088/1751-8113/49/2/02lt02
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发表时间：
2015
期刊：
Journal of Physics A: Mathematical and Theoretical
影响因子：
--
通讯作者：
R. Santachiara
R. Santachiara
中科院分区：
--
文献类型：
--
作者：
X. Cao;A. Rosso;R. Santachiara

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研究了单位圆上二维高斯自由场在Dirichlet边界条件下的极小统计量。相关的随机能量模型的自由能分布准确地计算在高温阶段，并示出满足的对偶属性，这使我们能够预测的最小值分布假设冻结的情况下。提供了数值试验。还考虑了关于球体上的GFF的相关问题。
We study minima statistics of the 2D Gaussian free field (GFF) on circles in the unit disk with Dirichlet boundary condition. Free energy distributions of the associated random energy models are exactly calculated in the high temperature phase, and shown to satisfy the duality property, which enables us to predict the minima distribution by assuming the freezing scenario. Numerical tests are provided. Related questions concerning the GFF on a sphere are also considered.