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

Dmitrii Krachun; Christoforos Panagiotis

doi:10.1214/24-AOP1730

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

Dmitrii Krachun, Christoforos Panagiotis

Princeton University

Research output: Contribution to journal › Article › peer-review

3 Downloads (Pure)

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/ log n). Previously, only a non-quantitative o(n)
bound was known from the work of Duminil-Copin and Hammond [DCH13]. 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

Original language	English
Pages (from-to)	1109-1125
Number of pages	21
Journal	Annals of Probability
Volume	54
Issue number	3
Early online date	20 Apr 2026
DOIs	https://doi.org/10.1214/24-AOP1730
Publication status	Published - 31 May 2026

Funding

This research is supported by the Swiss National Science Foundation and the NCCR SwissMAP.

Access to Document

10.1214/24-AOP1730

SAW_displacement (accepted author manuscript)Accepted author manuscript, 346 KB

Cite this

@article{fc20d2ae31f34c54829bfa90c989935a,

title = "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/ log n). Previously, only a non-quantitative o(n) bound was known from the work of Duminil-Copin and Hammond [DCH13]. 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",

author = "Dmitrii Krachun and Christoforos Panagiotis",

year = "2026",

month = may,

day = "31",

doi = "10.1214/24-AOP1730",

language = "English",

volume = "54",

pages = "1109--1125",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

number = "3",

}

TY - JOUR

T1 - Quantitative sub-ballisticity of self-avoiding walk on the hexagonal lattice

AU - Krachun, Dmitrii

AU - Panagiotis, Christoforos

PY - 2026/5/31

Y1 - 2026/5/31

N2 - 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/ log n). Previously, only a non-quantitative o(n) bound was known from the work of Duminil-Copin and Hammond [DCH13]. 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

AB - 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/ log n). Previously, only a non-quantitative o(n) bound was known from the work of Duminil-Copin and Hammond [DCH13]. 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

U2 - 10.1214/24-AOP1730

DO - 10.1214/24-AOP1730

M3 - Article

SN - 0091-1798

VL - 54

SP - 1109

EP - 1125

JO - Annals of Probability

JF - Annals of Probability

IS - 3

ER -

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

Abstract

Funding

Access to Document

Fingerprint

Cite this