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Algebra i Analiz, 2002, Volume 14, Issue 2, Pages 214–234 (Mi aa847)  

This article is cited in 50 scientific papers (total in 50 papers)

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The geometric Kannan–Lovász–Simonovits lemma, dimension-free estimates for volumes of sublevel sets of polynomials, and distribution of zeros of random analytic functions

F. Nazarova, M. Sodinb, A. Vol'berga

a Department of Mathematics, Michigan State University, East Lansing, MI, USA
b School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Israel
Received: 20.05.2001
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: F. Nazarov, M. Sodin, A. Vol'berg, “The geometric Kannan–Lovász–Simonovits lemma, dimension-free estimates for volumes of sublevel sets of polynomials, and distribution of zeros of random analytic functions”, Algebra i Analiz, 14:2 (2002), 214–234; St. Petersburg Math. J., 14:2 (2003), 351–366
Citation in format AMSBIB
\Bibitem{NazSodVol02}
\by F.~Nazarov, M.~Sodin, A.~Vol'berg
\paper The geometric Kannan--Lov\'asz--Simonovits lemma, dimension-free estimates for volumes of sublevel sets of polynomials, and distribution of zeros of random analytic functions
\jour Algebra i Analiz
\yr 2002
\vol 14
\issue 2
\pages 214--234
\mathnet{http://mi.mathnet.ru/aa847}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1925887}
\zmath{https://zbmath.org/?q=an:1030.60040}
\transl
\jour St. Petersburg Math. J.
\yr 2003
\vol 14
\issue 2
\pages 351--366
Linking options:
  • https://www.mathnet.ru/eng/aa847
  • https://www.mathnet.ru/eng/aa/v14/i2/p214
  • This publication is cited in the following 50 articles:
    1. Bhaskara A., Chen A., Perreault A., Vijayaraghavan A., “Smoothed Analysis For Tensor Methods in Unsupervised Learning”, Math. Program., 193:2 (2022), 549–599  crossref  mathscinet  isi
    2. G. I. Zelenov, “On distributions of trigonometric polynomials in Gaussian random variables”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 37 (2021), 77–92  mathnet  crossref
    3. V. I. Bogachev, “Chebyshev–Hermite polynomials and distributions of polynomials in Gaussian random variables”, Theory Probab. Appl., 66:4 (2022), 550–569  mathnet  crossref  crossref  zmath
    4. A. N. Kalinin, “Localization for Hyperbolic Measures on Infinite-Dimensional Spaces”, Funct. Anal. Appl., 55:4 (2021), 286–297  mathnet  crossref  crossref  isi
    5. Kosov E.D., “Total Variation Distance Estimates Via l-2-Norm For Polynomials in Log-Concave Random Vectors”, Int. Math. Res. Notices, 2021:21 (2021), 16494–16510  crossref  mathscinet  isi
    6. Tsuji H., “Dilation Type Inequalities For Strongly-Convex Sets in Weighted Riemannian Manifolds”, Anal. Geom. Metr. Spaces, 9:1 (2021), 219–253  crossref  mathscinet  isi
    7. Green J., “Lower Bounds on Lp Quasi-Norms and the Uniform Sublevel Set Problem”, Mathematika, 67:2 (2021), 296–323  crossref  mathscinet  isi
    8. G. I. Zelenov, “Drobnaya gladkost raspredelenii trigonometricheskikh polinomov na prostranstve s gaussovskoi meroi”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 31 (2020), 78–95  mathnet  crossref
    9. Kosov E.D., “On Fractional Regularity of Distributions of Functions in Gaussian Random Variables”, Fract. Calc. Appl. Anal., 22:5 (2019), 1249–1268  crossref  mathscinet  isi
    10. Bogachev I V., “Distributions of Polynomials in Many Variables and Nikolskii-Besov Spaces”, Real Anal. Exch., 44:1 (2019), 49–64  crossref  mathscinet  isi
    11. Bhaskara A., Chen A., Perreault A., Vijayaraghavan A., “Smoothed Analysis in Unsupervised Learning Via Decoupling”, 2019 IEEE 60Th Annual Symposium on Foundations of Computer Science (Focs 2019), Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Soc, 2019, 582–610  crossref  mathscinet  isi
    12. Brudnyi A., “Bernstein Type Inequalities For Restrictions of Polynomials to Complex Submanifolds of C-N”, J. Approx. Theory, 225 (2018), 106–147  crossref  mathscinet  zmath  isi  scopus
    13. Arutyunyan L.M., Kosov E.D., “Deviation of Polynomials From Their Expectations and Isoperimetry”, Bernoulli, 24:3 (2018), 2043–2063  crossref  mathscinet  zmath  isi  scopus
    14. Bogachev V.I., Kosov E.D., Zelenov G.I., “Fractional Smoothness of Distributions of Polynomials and a Fractional Analog of the Hardy-Landau-Littlewood Inequality”, Trans. Am. Math. Soc., 370:6 (2018), 4401–4432  crossref  mathscinet  zmath  isi  scopus
    15. Kosov E.D., “Fractional Smoothness of Images of Logarithmically Concave Measures Under Polynomials”, J. Math. Anal. Appl., 462:1 (2018), 390–406  crossref  mathscinet  zmath  isi
    16. Ganzburg M.I., “Polynomial Inequalities on Sets With K (M) -Concave Weighted Measures”, J. Anal. Math., 135:2 (2018), 389–411  crossref  mathscinet  zmath  isi  scopus
    17. Ganzburg M.I., “A multivariate Remez-type inequality with φ-concave weights”, Colloq. Math., 147:2 (2017), 221–240  crossref  mathscinet  zmath  isi  scopus
    18. Klartag Bo'az, “Needle Decompositions in Riemannian Geometry”, Mem. Am. Math. Soc., 249:1180 (2017), I–77  mathscinet  isi
    19. Temlyakov V. Tikhonov S., “Remez-Type and Nikol'Skii-Type Inequalities: General Relations and the Hyperbolic Cross Polynomials”, Constr. Approx., 46:3 (2017), 593–615  crossref  mathscinet  zmath  isi  scopus
    20. V. I. Bogachev, “Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures”, Russian Math. Surveys, 71:4 (2016), 703–749  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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