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Fluctuations of shapes of large areas under paths of random walks
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  • Published: December 1996

Fluctuations of shapes of large areas under paths of random walks

  • R. Dobrushin1 &
  • O. Hryniv2 nAff3 

Probability Theory and Related Fields volume 105, pages 423–458 (1996)Cite this article

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Summary

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.

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Author information

Author notes
  1. O. Hryniv

    Present address: E. Schrödinger International Institute for Mathematical Physics, Pasteurgasse 6/7, A-1090, Vienna, Austria

Authors and Affiliations

  1. Institute for Problems of Information Transmission, Russian Academy of Sciences, Ermolovoi 19, 103051, Moscow, Russia

    R. Dobrushin

  2. Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Naukova 3“b”, 290601, Lviv, Ukraine

    O. Hryniv

Authors
  1. R. Dobrushin
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  2. O. Hryniv
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Dobrushin, R., Hryniv, O. Fluctuations of shapes of large areas under paths of random walks. Probab. Th. Rel. Fields 105, 423–458 (1996). https://doi.org/10.1007/BF01191908

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  • Received: 30 December 1994

  • Revised: 06 March 1996

  • Issue Date: December 1996

  • DOI: https://doi.org/10.1007/BF01191908

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Mathematics Subject Classification (1991)

  • 60F17
  • 60F10
  • 60J15
  • 82B24
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