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SIGMA, 2011, Volume 7, 022, 12 pp.
(Mi sigma580)
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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
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http://emis.mi.ras.ru/journals/SIGMA/2011/022/
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ArXiv:
0912.2135
MSC: 11D25; 11R29; 26B20; 81Q99 Received: January 12, 2011; in final form February 28, 2011; Published online March 4, 2011
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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
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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:
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JETP Letters, 95:11 (2012), 586–593
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A. Yu. Morozov, “Challenges of $\beta$-deformation”, Theoret. and Math. Phys., 173:1 (2012), 1417–1437
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Lasserre, Jean B., “Level Sets and NonGaussian Integrals of Positively Homogeneous Functions”, INTERNATIONAL GAME THEORY REVIEW, 17:1 (2015), 1540001
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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
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