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SIGMA, 2011, Volume 7, 022, 12 pp. (Mi sigma580)  

This article is cited in 4 scientific papers (total in 4 papers)

Beyond the Gaussian

Kazuyuki Fujii

Department of Mathematical Sciences, Yokohama City University, Yokohama, 236-0027 Japan

Abstract: In this paper we present a non-Gaussian integral based on a cubic polynomial, instead of a quadratic, and give a fundamental formula in terms of its discriminant. It gives a mathematical reinforcement to the recent result by Morozov and Shakirov. We also present some related results. This is simply one modest step to go beyond the Gaussian but it already reveals many obstacles related with the big challenge of going further beyond the Gaussian.

Keywords: non-Gaussian integral; renormalized integral; discriminant; cubic equation

DOI: https://doi.org/10.3842/SIGMA.2011.022

Full text: PDF file (298 kB)
Full text: http://emis.mi.ras.ru/journals/SIGMA/2011/022/
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Bibliographic databases:

ArXiv: 0912.2135
MSC: 11D25; 11R29; 26B20; 81Q99
Received: January 12, 2011; in final form February 28, 2011; Published online March 4, 2011
Language:

Citation: Kazuyuki Fujii, “Beyond the Gaussian”, SIGMA, 7 (2011), 022, 12 pp.

Citation in format AMSBIB
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\by Kazuyuki Fujii
\paper Beyond the Gaussian
\jour SIGMA
\yr 2011
\vol 7
\papernumber 022
\totalpages 12
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\crossref{https://doi.org/10.3842/SIGMA.2011.022}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2804574}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855238265}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. JETP Letters, 95:11 (2012), 586–593  mathnet  crossref  isi  elib  elib
    2. A. Yu. Morozov, “Challenges of $\beta$-deformation”, Theoret. and Math. Phys., 173:1 (2012), 1417–1437  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    3. Lasserre, Jean B., “Level Sets and NonGaussian Integrals of Positively Homogeneous Functions”, INTERNATIONAL GAME THEORY REVIEW, 17:1 (2015), 1540001  crossref  mathscinet  zmath  elib  scopus
    4. Lasserre J., “Introduction to Polynomial and Semi-Algebraic Optimization”, Introduction to Polynomial and Semi-Algebraic Optimization, Cambridge Texts in Applied Mathematics, Cambridge Univ Press, 2015, 1–339  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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