Let $(S_n )_{n \in \mathbb {N}_0} be a random walk on the integers
having bounded steps. The self-repellent (resp., self-avoiding) walk is a
sequence of transformed path measures which discourage (resp., forbid)
self-intersections. This is used as a model for polymers. Previously, we proved
a law of large numbers; that is, we showed the convergence of $|S_n | /n$
toward a positive number $\theta$ under the polymer measure. The present paper
proves a classical central limit theorem for the self-repellent and
self-avoiding walks; that is, we prove the asymptotic normality of $(S_n -
\theta_n) / \sqrt{n}$ for largen. The proof refines and continues results
and techniques developed previously.
Publié le : 1996-04-14
Classification:
Central limit theorem,
self-avoiding and self-repellent random walk,
ergodic Markov chains,
large deviations,
60F05,
58E30,
60F10,
60J15
@article{1039639376,
author = {K\"onig, Wolfgang},
title = {A central limit theorem for a one-dimensional polymer
measure},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 1012-1035},
language = {en},
url = {http://dml.mathdoc.fr/item/1039639376}
}
König, Wolfgang. A central limit theorem for a one-dimensional polymer
measure. Ann. Probab., Tome 24 (1996) no. 2, pp. 1012-1035. http://gdmltest.u-ga.fr/item/1039639376/