Affordable Access

Publisher Website

Self-Avoiding Walk is Sub-Ballistic

Authors
Journal
Communications in Mathematical Physics
0010-3616
Publisher
Springer-Verlag
Publication Date
Volume
324
Issue
2
Identifiers
DOI: 10.1007/s00220-013-1811-1

Abstract

We prove that self-avoiding walk on ℤ is sub-ballistic in any dimension d ≥ 2. That is,writing {double pipe}u{double pipe} for the Euclidean norm of u ∈ ℤ, and P for the uniform measure on self-avoiding walks γ: {0,...,n} → ℤ for which γ = 0, we show that,for each v > 0, there exists ε > 0 such that, for each n ∈ ℕ, P(max {double pipe}γ{double pipe}: 0 ≤ k ≤ n} ≥ vn) ≤ e. © 2013 Springer-Verlag Berlin Heidelberg.

There are no comments yet on this publication. Be the first to share your thoughts.