Quantitative sub-ballisticity of self-avoiding walk on the hexagonal lattice
Abstract
We prove quantitative sub-ballisticity for the self-avoiding walk on the hexagonal lattice. Namely, we show that, with high probability, a self-avoiding walk of length n does not exit a ball of radius O(n/logn). Previously, only a nonquantitative o(n) bound was known from the work of Duminil-Copin and Hammond (Comm. Math. Phys. 324 (2013) 401–423). As an important ingredient of the proof, we show that at criticality the partition function of bridges of height T decays polynomially fast to 0 as T tends to infinity, which we believe to be of independent interest.
Fields of Study & Subjects
Markov Chains and Monte Carlo Methods
Stochastic processes and statistical mechanics
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- The Annals of Probability
- Volume
- 54
- Issue
- 3
- Publication date
- 21 April 2026
- Language
- EN