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Random trees and moduli of curves

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Asymptotic Combinatorics with Applications to Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1815))

Abstract

This is an expository account of the proof of Kontsevich’s combinatorial formula for intersections on moduli spaces of curves following the paper [14].It is based on the lectures I gave on the subject in St. Petersburg in July of 2001.

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References

  1. Arnold, V.I.:Topological classification of complex trigonometric polynomials and the combinatorics of graphs with an identical number of vertices and edges.Funct.Anal.Appl.,30, no.1,1–14 (1996)

    Google Scholar 

  2. Di Francesco, P.: 2-D quantum and topological gravities,matrix models,and integrable differential systems.The Painlevé Property, Springer-Verlag, 229–285(1999)

    Google Scholar 

  3. Ekedahl, T., Lando, S., Shapiro, M., Vainshtein, A.:Hurwitz numbers and intersections on moduli spaces of curves.Invent.Math.,146,no.2, 297–327 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fantechi, B., Pandharipande, R. Stable maps and branch divisors.math.AG/9905104

    Google Scholar 

  5. Fulton, W.: Intersection theory.Springer-Verlag (1998)

    Google Scholar 

  6. Graber, T., Pandharipande, R.:Localization of virtual classes. Invent.Math.,135, 487–518 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Graber, T., Vakil, R.: Hodge integrals and Hurwitz numbers via virtual localization.math.AG/0003028

    Google Scholar 

  8. Harris, J., Morrison, I.: Moduli of Curves. Springer-Verlag (1998)

    Google Scholar 

  9. Kontsevich, M.: Intersection theory on the moduli space of curves and the matrix Airy function. Commun.Math.Phys.,147,1–23 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  10. Okounkov, A.:Random matrices and random permutations.IMRN, no.20, 1043–1095 (2000)

    Google Scholar 

  11. Okounkov, A.: Infinite wedge and random partitions.Selecta Math.,New Ser., 7, 1–25 (2001)

    Article  MathSciNet  Google Scholar 

  12. Okounkov, A.: Toda equations for Hurwitz numbers. Math.Res.Lett.,7, no.4, 447–453 (2000)

    MATH  MathSciNet  Google Scholar 

  13. Okounkov, A.: Generating functions for intersection numbers on moduli spaces of curves.IMRN, no.18, 933–957 (2002)

    Google Scholar 

  14. Okounkov, A., Pandharipande, R.: Gromov—Witten theory, Hurwitz numbers, and matrix models,I.math.AG/0101147

    Google Scholar 

  15. Okounkov, A., Pandharipande, R.: in preparation

    Google Scholar 

  16. Pitman, J.:Enumeration of trees and forests related to branching processes and random walks.DIMACS Series in Discrete Mathematics and Theoretical Computer Science,41 (1998)

    Google Scholar 

  17. Stanley, R.: Enumerative combinatorics,Vol.2.Cambridge Studies in Advanced Mathematics,62, Cambridge University Press, Cambridge (1999)

    Google Scholar 

  18. Tracy, C.A., Widom, H.:Level-spacing distributions and the Airy kernel. Commun.Math.Phys.,159, 151–174 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  19. Witten, E.: Two-dimensional gravity and intersection theory on moduli space.Surveys in Diff.Geom.,1, 243–310 (1991)

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California at Berkeley, Evans Hall #3840, Berkeley, CA, 947203840, USA

    Andrei Okounkov

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  1. Andrei Okounkov
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Editors and Affiliations

  1. St. Petersburg Department of the Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191011, St. Petersburg, Russia

    Anatoly M. Vershik

  2. St. Petersburg Department of the Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191011, St. Petersburg, Russia

    Yuri Yakubovich

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Okounkov, A. (2003). Random trees and moduli of curves. In: Vershik, A.M., Yakubovich, Y. (eds) Asymptotic Combinatorics with Applications to Mathematical Physics. Lecture Notes in Mathematics(), vol 1815. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44890-X_5

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  • DOI: https://doi.org/10.1007/3-540-44890-X_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40312-8

  • Online ISBN: 978-3-540-44890-7

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