Work

Backbone exponent for two-dimensional percolation

Year: 2023

Type: preprint

Abstract: We derive an exact expression for the celebrated backbone exponent for Bernoulli percolation in dimension two at criticality. It turns out to be a root of an elementary function. Contrary to previously known arm exponents for this model, which are all rational, it has a transcendental value. Our derivation relies on the connection to the SLE$_κ$ bubble measure, the coupling between SLE and Liouville quantum gravity, and the integrability of Liouville conformal field theory. Along the way, we derive a formula not only for $κ=6$ (corresponding to percolation), but for all $κ\in (4,8)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2309.05050

Authors: Nolin, Pierre, Qian, Wei, Sun, Xin, Zhuang, Zijie

Institutions: City University of Hong Kong, Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay, Peking University, University of Pennsylvania

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, University of Pennsylvania, City University of Hong Kong

Awards: Geometric, Optimizational and Spectral Problems in Large Random Structures, CAREER: Liouville Quantum Gravity, Two-Dimensional Random Geometry, and Conformal Field Theory

OpenAlex ID: W4386648011

Cites:

Cited by: 5

Related to: 10