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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 384, Pages 154–175 (Mi znsl3888)  
This article is cited in 4 scientific papers (total in 5 papers)

On random surface area

D. N. Zaporozhets, I. A. Ibragimov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (285 kB) Citations (5)
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Abstract: Consider a random smooth Gaussian field $G(x)\colon F\to\mathbb R$, where $F$ is a compact in $\mathbb R^d$. We derive a formula for average area of a surface set by the equation $G(x)=0$ and give some applications. As an auxiliary result we obtain an integral expression for area of a surface induced by zeros of any non-random smooth field. Bibl. 13 titles.
Key words and phrases: random Gaussian field, surface area, Favard measure, coarea formula, Rice formula.
Received: 10.11.2010
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 176, Issue 2, Pages 190–202
DOI: https://doi.org/10.1007/s10958-011-0409-4
Bibliographic databases:
Document Type: Article
UDC: 519
Language: Russian
Citation: D. N. Zaporozhets, I. A. Ibragimov, “On random surface area”, Probability and statistics. Part 16, Zap. Nauchn. Sem. POMI, 384, POMI, St. Petersburg, 2010, 154–175; J. Math. Sci. (N. Y.), 176:2 (2011), 190–202
Citation in format AMSBIB
\Bibitem{ZapIbr10}
\by D.~N.~Zaporozhets, I.~A.~Ibragimov
\paper On random surface area
\inbook Probability and statistics. Part~16
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 384
\pages 154--175
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3888}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 176
\issue 2
\pages 190--202
\crossref{https://doi.org/10.1007/s10958-011-0409-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959538404}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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