Quantitative sub-ballisticity of self-avoiding walk on the hexagonal lattice

2023/10/26 by Krachun, Dmitrii, Panagiotis, Christoforos
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2310.17299

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 non-quantitative o(n) bound was known from the work of Duminil-Copin and Hammond \citeDCH13. 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.

Related

• Lectures on Self-Avoiding Walks
• On self-avoiding polygons and walks: counting, joining and closing
• On the theorem of Duminil-Copin and Smirnov about the number of self-avoiding walks in the hexagonal lattice
• Self-avoiding walks and polygons confined to a square
• Self-avoiding walk is ballistic on graphs with more than one end