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April 1996 A central limit theorem for a one-dimensional polymer measure
Wolfgang König
Ann. Probab. 24(2): 1012-1035 (April 1996). DOI: 10.1214/aop/1039639376


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 large n. The proof refines and continues results and techniques developed previously.


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Wolfgang König. "A central limit theorem for a one-dimensional polymer measure." Ann. Probab. 24 (2) 1012 - 1035, April 1996.


Published: April 1996
First available in Project Euclid: 11 December 2002

zbMATH: 0862.60018
MathSciNet: MR1404542
Digital Object Identifier: 10.1214/aop/1039639376

Primary: 60F05
Secondary: 58E30 , 60F10 , 60J15

Keywords: central limit theorem , Ergodic Markov chains , large deviations , self-avoiding and self-repellent random walk

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 2 • April 1996
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