MAXIMUM AND COUPLING OF THE SINE-GORDON FIELD

• 成果类型: Article
• 署名作者: Bauerschmidt, Roland; Hofstetter, Michael
• 署名单位: University of Cambridge
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1537
• 发表日期: 2022
• 页码: 455-508
• 关键词: convergence; equation; LAW; regions

摘要

For 0 < beta < 6 pi, we prove that the distribution of the centred maximum of the e-regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted Gumbel distribution as epsilon -> 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.