Almost sure convergence of Liouville first passage percolation

• 成果类型: Article
• 署名作者: Devlin, Charles
• 署名单位: University of Chicago
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01323-y
• 发表日期: 2025
• 页码: 247-288
• 关键词: quantum-gravity

摘要

Liouville first passage percolation (LFPP) with parameter xi > 0 is the family of random distance functions (metrics) (D-h(is an element of))is an element of > 0 on obtained heuristically by integrating e(xi h) along paths, where h is a variant of the Gaussian free field. There is a critical value xi(crit )approximate to 0.41 such that for xi is an element of (0, xi(crit)), appropriately rescaled LFPP converges in probability uniformly on compact subsets of C to a limiting metric D-h on gamma-Liouville quantum gravity with gamma = gamma(xi) is an element of (0,2). We show that the convergence is almost sure, giving an affirmative answer to a question posed by Gwynne and Miller (Invent. Math. 223, 213-333 (2021) [math.PR]).