2025/02/13 by Yichao Huang, Huang, Yichao
Computer Science · Mathematics · #Chaos-based Image/Signal Encryption #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2502.09121
openalex publication_date 2025/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the first part of a series of papers devoted to studying the right tail profile of a bulk Gaussian multiplicative chaos measure with uniform singularity on the boundary. We investigate the bulk/boundary quotients of Gaussian multiplicative chaos measures appearing in boundary Liouville conformal field theory, for which we establish preliminary joint moment bounds. These moment bounds will be a crucial ingredient in establishing the right tail profile of the bulk Gaussian multiplicative chaos measure in subsequent papers. The main idea is to implement the so-called localization trick at the boundary, and we also record a useful generalization of Kahane's convexity inequality, which is of independent interest. The study of the universal tail profiles of general bulk measures and bulk/boundary quotients as well as connections to integrability results of boundary Liouville conformal field theory will be pursued in subsequent papers.