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

This article is cited in 39 scientific papers (total in 39 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

Full text: PDF file (977 kB)

English version:
St. Petersburg Mathematical Journal, 2003, 14:2, 351–366

Bibliographic databases:
Received: 20.05.2001

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://www.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


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    This publication is cited in the following articles:
    1. Nazarov F., Sodin M., Volberg A., “Local dimension-free estimates for volumes of sublevel sets of analytic functions”, Israel J. Math., 133 (2003), 269–283  crossref  mathscinet  zmath  isi  scopus
    2. Fradelizi M., Guédon O., “The extreme points of subsets of $s$-concave probabilities and a geometric localization theorem”, Discrete Comput. Geom., 31:2 (2004), 327–335  crossref  mathscinet  zmath  isi  scopus
    3. Bastero J., Romance M., “Random vectors satisfying Khinchine–Kahane type inequalities for linear and quadratic forms”, Mathematische Nachrichten, 278:9 (2005), 1015–1024  crossref  mathscinet  zmath  isi  scopus
    4. Bobkov S. G., Zegarlinski B., Entropy bounds and isoperimetry, Mem. Amer. Math. Soc., 176, no. 829, 2005, x+69 pp.  mathscinet  isi  elib
    5. Sodin M.“,Zeroes of Gaussian analytic functions”, European Congress of Mathematics, 2005, 445–458  mathscinet  zmath  isi
    6. Fradelizi M., Guedon O., “A generalized localization theorem and geometric inequalities for convex bodies”, Advances in Mathematics, 204:2 (2006), 509–529  crossref  mathscinet  zmath  isi  scopus
    7. J. Math. Sci. (N. Y.), 152:6 (2008), 826–839  mathnet  crossref
    8. Bobkov S. G., “Large deviations and isoperimetry over convex probability measures with heavy tails”, Electron. J. Probab., 12 (2007), 1072–1100 (electronic)  crossref  mathscinet  zmath  isi  elib  scopus
    9. Brudnyi A., “On local behavior of holomorphic functions along complex submanifolds of C–N supercript stop”, Inventiones Mathematicae, 173:2 (2008), 315–363  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. Fradelizi M., “Concentration inequalities for $s$-concave measures of dilations of Borel sets and applications”, Electron. J. Probab., 14:71 (2009), 2068–2090  crossref  mathscinet  zmath  isi  scopus
    11. Klartag B., “A Berry-Esseen type inequality for convex bodies with an unconditional basis”, Probab. Theory Related Fields, 145:1-2 (2009), 1–33  crossref  mathscinet  zmath  isi  scopus
    12. Milman E., “Isoperimetric Bounds on Convex Manifolds”, Concentration, Functional Inequalities and Isoperimetry, Contemporary Mathematics, 545, 2011, 195–208  crossref  mathscinet  zmath  isi
    13. Boros N., Janakiraman P., Volberg A., “Sharp L-P-bounds for a perturbation of Burkholder's Martingale Transform”, C R Math Acad Sci Paris, 349:5–6 (2011), 303–307  crossref  mathscinet  zmath  isi  scopus
    14. Janakiraman P., “Orthogonality in Complex Martingale Spaces and Connections with the Beurling-Ahlfors Transform”, Ill. J. Math., 54:4, SI (2012), 1509–1563  mathscinet  isi
    15. Akopyan A., Karasev R., “Kadets-Type Theorems for Partitions of a Convex Body”, Discret. Comput. Geom., 48:3 (2012), 766–776  crossref  mathscinet  zmath  isi  elib  scopus
    16. Boros N., Janakiraman P., Volberg A., “Perturbation of Burkholder's Martingale Transform and Monge-Ampere Equation”, Adv. Math., 230:4-6 (2012), 2198–2234  crossref  mathscinet  zmath  isi  scopus
    17. Cwikel M., Sagher Y., Shvartsman P., “A New Look at the John-Nirenberg and John-Stromberg Theorems for Bmo”, J. Funct. Anal., 263:1 (2012), 129–166  crossref  mathscinet  zmath  isi  elib  scopus
    18. Milman E., “A Proof of Bobkov's Spectral Bound for Convex Domains via Gaussian Fitting and Free Energy Estimation”, Analysis and Geometry of Metric Measure Spaces, CRM Proceedings & Lecture Notes, 56, eds. Dafni G., McCann R., Stancu A., Amer Mathematical Soc, 2013, 181–196  crossref  mathscinet  zmath  isi
    19. Boros N., Szekelyhidi Jr. Laszlo, Volberg A., “Laminates Meet Burkholder Functions”, J. Math. Pures Appl., 100:5 (2013), 687–700  crossref  mathscinet  zmath  isi  scopus
    20. Brudnyi A., “L-Q Norm Inequalities for Analytic Functions Revisited”, J. Approx. Theory, 179 (2014), 24–32  crossref  mathscinet  zmath  isi  scopus
    21. Eldan R., Klartag Bo'az, “Dimensionality and the Stability of the Brunn-Minkowski Inequality”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 13:4 (2014), 975–1007  mathscinet  zmath  isi
    22. Bradshaw Z., Grujie Z., “Blow-Up Scenarios For the 3D Navier–Stokes Equations Exhibiting Sub-Criticality With Respect To the Scaling of One-Dimensional Local Sparseness”, J. Math. Fluid Mech., 16:2 (2014), 321–334  crossref  mathscinet  zmath  isi  scopus
    23. L. M. Arutyunyan, E. D. Kosov, “Estimates for integral norms of polynomials on spaces with convex measures”, Sb. Math., 206:8 (2015), 1030–1048  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    24. Kosov E.D., “Lower Estimates of Measure of Deviation of Polynomials From Mathematical Expectations”, Dokl. Math., 92:3 (2015), 698–700  crossref  mathscinet  zmath  isi  elib  scopus
    25. Adamczak R., Wolff P., “Concentration Inequalities For Non-Lipschitz Functions With Bounded Derivatives of Higher Order”, Probab. Theory Relat. Field, 162:3-4 (2015), 531–586  crossref  mathscinet  zmath  isi  elib  scopus
    26. Bobkov S.G., Melbourne J., “Localization For Infinite-Dimensional Hyperbolic Measures”, Dokl. Math., 91:3 (2015), 297–299  crossref  mathscinet  zmath  isi  scopus
    27. Arutyunyan L.M., Kosov E.D., “Polynomials on Spaces With Logarithmically Concave Measures”, Dokl. Math., 91:1 (2015), 72–75  crossref  mathscinet  zmath  isi  elib  scopus
    28. 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  adsnasa  isi  elib
    29. L. M. Arutyunyan, “Absolute Continuity of Distributions of Polynomials on Spaces with Log-Concave Measures”, Math. Notes, 101:1 (2017), 31–38  mathnet  crossref  crossref  mathscinet  isi  elib
    30. Ganzburg M.I., “Multivariate polynomial inequalities of different
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