On the scaling limit of planar selfavoiding walk
Abstract
A planar selfavoiding walk (SAW) is a nearest neighbor random walk path in the square lattice with no selfintersection. A planar selfavoiding polygon (SAP) is a loop with no selfintersection. In this paper we present conjectures for the scaling limit of the uniform measures on these objects. The conjectures are based on recent results on the stochastic Loewner evolution and nondisconnecting Brownian motions. New heuristic derivations are given for the critical exponents for SAWs and SAPs.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2002
 DOI:
 10.48550/arXiv.math/0204277
 arXiv:
 arXiv:math/0204277
 Bibcode:
 2002math......4277L
 Keywords:

 Probability;
 Mathematical Physics;
 60K35;
 82B41
 EPrint:
 Fractal geometry and applications: a jubilee of Beno\^it Mandelbrot, Part 2, 339364, Proc. Sympos. Pure Math., 72, Part 2, Amer. Math. Soc., Providence, RI, 2004