Geodesic
A Lower Bound for the End-to-End Distance of the Self-Avoiding Walk
Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 113-118

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2012-022-6
Mots-clés : 82B41, 60D05, 60K35, self-avoiding walk, critical exponent 
Madras, Neal. A Lower Bound for the End-to-End Distance of the Self-Avoiding Walk. Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 113-118. doi: 10.4153/CMB-2012-022-6
@article{10_4153_CMB_2012_022_6,
     author = {Madras, Neal},
     title = {A {Lower} {Bound} for the {End-to-End} {Distance} of the {Self-Avoiding} {Walk}},
     journal = {Canadian mathematical bulletin},
     pages = {113--118},
     year = {2014},
     volume = {57},
     number = {1},
     doi = {10.4153/CMB-2012-022-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-022-6/}
}
TY  - JOUR
AU  - Madras, Neal
TI  - A Lower Bound for the End-to-End Distance of the Self-Avoiding Walk
JO  - Canadian mathematical bulletin
PY  - 2014
SP  - 113
EP  - 118
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-022-6/
DO  - 10.4153/CMB-2012-022-6
ID  - 10_4153_CMB_2012_022_6
ER  - 
%0 Journal Article
%A Madras, Neal
%T A Lower Bound for the End-to-End Distance of the Self-Avoiding Walk
%J Canadian mathematical bulletin
%D 2014
%P 113-118
%V 57
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-022-6/
%R 10.4153/CMB-2012-022-6
%F 10_4153_CMB_2012_022_6

[1] [1] Brydges, D. and Slade, G., Renormalisation group analysis of weakly self-avoiding walk in dimensionsfour and higher. In: Proceedings of the International Congress of Mathematicians, Volume IV, Hindustan Book Agency, New Delhi, 2010, pp. 2232–2257. Google Scholar

[2] [2] Duminil-Copin, H. and Hammond, A., Self-avoiding walk is sub-ballistic. arxiv:1205.0401 Google Scholar

[3] [3] Hara, T. and Slade, G., Self-avoiding walk in five or more dimensions. I. The critical behaviour. Comm. Math. Phys. 147 (1992), no. 1, 101–136. Google Scholar | DOI

[4] [4] Hara, T. and Slade, G., The lace expansion for self-avoiding walk in five or more dimensions. Rev. Math. Phys. 4 (1992), no. 2, 235–327. Google Scholar | DOI

[5] [5] Madras, N. and Slade, G., The self-avoiding walk. Probability and its applications. Birkhäuser, Boston, 1993. Google Scholar

[6] [6] Slade, G., The lace expansion and its applications. Lectures from the 34th Summer School onProbability Theory held in Saint-Flour, July 6–24, 2004. Lecture Notes in Mathematics, 1879. Springer-Verlag, Berlin, 2006. Google Scholar

[7] [7] Slade, G., The self-avoiding walk: A brief survey. In: Surveys in stochastic processes, EMS Ser. Congr. Rep., European Mathematical Society, Zurich, 2011, pp. 189–199. Google Scholar

[8] [8] Vanderzande, C., Lattice models of polymers. Cambridge University Press, Cambridge, 1998 Google Scholar

Cité par Sources :