A Lower Bound for the End-to-End Distance of the Self-Avoiding Walk. Issue 1 (14th March 2014)

• Record Type: Journal Article
• Authors: Madras, Neal
• Is Part Of: Canadian mathematical bulletin =. Volume 57:Issue 1(2014)
• Page Start: 113
• Page End: 118
• Publication Date: 2014-03-14
• Subjects: 82B41 -- 60D05 -- 60K35; self-avoiding walk -- critical exponent; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2012-022-6
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: For an $N$ -step self-avoiding walk on the hypercubic lattice ${{Z}^{d}}$, we prove that the meansquare end-to-end distance is at least ${{N}^{4/(3d)}}$ times a constant. This implies that the associated critical exponent $v$ is at least $2/(3d)$, assuming that $v$ exists.