论文标题
正弦山脉的最大和耦合
Maximum and coupling of the sine-Gordon field
论文作者
论文摘要
对于$ 0 <β<6π$，我们证明了二维圆环上$ε$的连续正弦 - 戈登场的中心最大值分布收敛到随机移动的gumbel分布，为$ε\ to $ε\至0 $。我们的证明依赖于正弦波场所有尺度上的强耦合与高斯自由场，独立感兴趣的耦合以及现有方法的扩展，以最大程度地提高晶格高斯自由场。
For $0<β<6π$, we prove that the distribution of the centred maximum of the $ε$-regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted Gumbel distribution as $ε\to 0$. Our proof relies on a strong coupling at all scales of the sine-Gordon field with the Gaussian free field, of independent interest, and extensions of existing methods for the maximum of the lattice Gaussian free field.
