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Fluctuations of shapes of large areas under paths of random walks.

Dobrushin, R. and Hryniv, O. (1996) 'Fluctuations of shapes of large areas under paths of random walks.', Probability theory and related fields., 105 (4). pp. 423-458.


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.

Item Type:Article
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Date accepted:No date available
Date deposited:13 June 2014
Date of first online publication:December 1996
Date first made open access:No date available

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