A UNIVERSALITY RESULT FOR SUBCRITICAL COMPLEX GAUSSIAN MULTIPLICATIVE CHAOS

• 成果类型: Article
• 署名作者: Lacoin, Hubert
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1677
• 发表日期: 2022
• 页码: 269-293
• 关键词: glassy phase; CONVERGENCE; maximum

摘要

In the present paper, we show that (under some minor technical assumption) Complex Gaussian multiplicative chaos defined as the complex exponential of a log-correlated Gaussian field can be obtained by taking the limit of the exponential of the field convoluted with a smoothing kernel. We consider two types of chaos: e(gamma)(X) for a log correlated field X and gamma = alpha + i beta, alpha, beta is an element of R and e(alpha X+)(i beta)(Y) for X and Y two independent fields with alpha, beta is an element of R. Our result is valid in the range P-sub := {alpha(2) + beta(2) < d} boolean OR {vertical bar alpha vertical bar is an element of (root d/2, root 2d) and vertical bar beta vertical bar < root 2d - vertical bar alpha vertical bar}, which, up to boundary, is conjectured to be optimal.