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Fluctuations of shapes of large areas under paths of random walks

Dobrushin, R.; Hryniv, O.

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Authors

R. Dobrushin



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 Mar 29, 2024
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

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