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TMF, 2001, Volume 127, Number 2, Pages 179–252 (Mi tmf455)  

This article is cited in 1 scientific paper (total in 1 paper)

Matrix Models: Geometry of Moduli Spaces and Exact Solutions

L. O. Chekhov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We study the connection between characteristics of moduli spaces of Riemann surfaces with marked points and matrix models. The Kontsevich matrix model describes intersection indices on continuous moduli spaces, and the Kontsevich–Penner matrix model describes intersection indices on discretized moduli spaces. Analyzing the constraint algebras satisfied by various generalized Kontsevich matrix models, we derive time transformations that establish exact relations between different models appearing in mathematical physics. We solve the Hermitian one-matrix model using the moment technique in the genus expansion and construct a recursive procedure for solving this model in the double scaling limit.

DOI: https://doi.org/10.4213/tmf455

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English version:
Theoretical and Mathematical Physics, 2001, 127:2, 557–618

Bibliographic databases:

Document Type: Article
Received: 22.01.2001

Citation: L. O. Chekhov, “Matrix Models: Geometry of Moduli Spaces and Exact Solutions”, TMF, 127:2 (2001), 179–252; Theoret. and Math. Phys., 127:2 (2001), 557–618

Citation in format AMSBIB
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\transl
\jour Theoret. and Math. Phys.
\yr 2001
\vol 127
\issue 2
\pages 557--618
\crossref{https://doi.org/10.1023/A:1010471418775}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. B. Bogatyrev, “Combinatorial description of a moduli space of curves and of extremal polynomials”, Sb. Math., 194:10 (2003), 1451–1473  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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