UNIFORM SPANNING TREE IN TOPOLOGICAL POLYGONS, PARTITION FUNCTIONS FOR SLE(8), AND CORRELATIONS IN c =-2 LOGARITHMIC CFT

• 成果类型: Article
• 署名作者: Liu, Mingchang; Peltola, Eveliina; Wu, Hao
• 署名单位: Royal Institute of Technology; University of Bonn; Tsinghua University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1700
• 发表日期: 2025
• 页码: 23-78
• 关键词: erased random-walks; conformal-invariance; percolation; symmetry; LIMITS; plane

摘要

We find explicit SLE(8) partition functions for the scaling limits of Peano curves in the uniform spanning tree (UST) in topological polygons with general boundary conditions. They are given in terms of Coulomb gas integral formulas, which can also be expressed in terms of determinants involving a-periods of a hyperelliptic Riemann surface. We also identify the crossing probabilities for the UST Peano curves as ratios of these partition functions. The partition functions are interpreted as correlation functions in a logarithmic conformal field theory (log-CFT) of central charge c = -2. Indeed, it is clear from our results that this theory is not a minimal model and exhibits logarithmic phenomena-the limit functions have logarithmic asymptotic behavior, that we calculate explicitly. General fusion rules for them could also be inferred from the explicit formulas. The discovered algebraic structure matches the known Virasoro staggered module classification, so in this sense, we give a direct probabilistic construction for correlation functions in a logCFT of central charge -2 describing the UST model.