Fluctuations of shapes of large areas under paths of random walks

Dobrushin, R.; Hryniv, O.

Abstract

We discuss statistical properties of random walks conditioned by fixing a large area under their paths. We prove the functional central limit theorem (invariance principle) for these conditional distributions. The limiting Gaussian measure coincides with the conditional probability distribution of certain timenonhomogeneous Gaussian random process obtained by an integral transformation of the white noise. From the point of view of statistical mechanics the studied problem is the problem of describing the fluctuations of the phase boundary in the one-dimensional SOS-model.

Citation

Dobrushin, R., & Hryniv, O. (1996). Fluctuations of shapes of large areas under paths of random walks. Probability Theory and Related Fields, 105(4), 423-458. https://doi.org/10.1007/bf01191908

• Journal Article Type: Article
• Publication Date: Dec 1, 1996
• Deposit Date: Jun 13, 2014
• Publicly Available Date: Jun 13, 2014
• Journal: Probability Theory and Related Fields
• Print ISSN: 0178-8051
• Electronic ISSN: 1432-2064
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 105
• Issue: 4
• Pages: 423-458
• DOI: https://doi.org/10.1007/bf01191908
• Public URL: https://durham-repository.worktribe.com/output/1558365