RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 1999, Volume 54, Issue 4(328), Pages 3–46 (Mi umn178)  

This article is cited in 9 scientific papers (total in 9 papers)

Probability related to quantum gravity. Planar gravity

V. A. Malyshev

M. V. Lomonosov Moscow State University

Abstract: The stochastic dynamics preserving an equilibrium distribution of quantum gravity is considered. This is the first detailed theoretical investigation of this dynamics (earlier it was used for Monte-Carlo simulation). The main result is related to the existence and certain properties of local correlation functions in the thermodynamic limit. At the same time, the paper can serve as a mathematical introduction to quantum gravity because we give a rigorous exposition of quantum gravity in the case of planar pure gravity. We mainly use the combinatorial approach instead of matrix models, which are more popular in physics, and the central point is the famous exponent $\alpha =-\frac72$.

DOI: https://doi.org/10.4213/rm178

Full text: PDF file (488 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1999, 54:4, 685–728

Bibliographic databases:

UDC: 519.2
MSC: Primary 83C45, 81T40; Secondary 60K35, 83C27, 05C30, 57M20, 60J15, 60J05, 82B10, 6
Received: 18.09.1998

Citation: V. A. Malyshev, “Probability related to quantum gravity. Planar gravity”, Uspekhi Mat. Nauk, 54:4(328) (1999), 3–46; Russian Math. Surveys, 54:4 (1999), 685–728

Citation in format AMSBIB
\Bibitem{Mal99}
\by V.~A.~Malyshev
\paper Probability related to quantum gravity. Planar gravity
\jour Uspekhi Mat. Nauk
\yr 1999
\vol 54
\issue 4(328)
\pages 3--46
\mathnet{http://mi.mathnet.ru/umn178}
\crossref{https://doi.org/10.4213/rm178}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1741277}
\zmath{https://zbmath.org/?q=an:0977.83028}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1999RuMaS..54..685M}
\transl
\jour Russian Math. Surveys
\yr 1999
\vol 54
\issue 4
\pages 685--728
\crossref{https://doi.org/10.1070/rm1999v054n04ABEH000178}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000085500400001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0033262832}


Linking options:
  • http://mi.mathnet.ru/eng/umn178
  • https://doi.org/10.4213/rm178
  • http://mi.mathnet.ru/eng/umn/v54/i4/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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:
    1. Malyshev, VA, “Quantum grammars”, Journal of Mathematical Physics, 41:7 (2000), 4508  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Malyshev V., “Gibbs families”, Mathematics and Computer Science - Algorithms, Trees, Combinatorics and Probabilities, Trends in Mathematics, 2000, 295–304  mathscinet  zmath  isi
    3. V. A. Malyshev, A. A. Yambartsev, A. A. Zamyatin, “Two-dimensional Lorentzian models”, Mosc. Math. J., 1:3 (2001), 439–456  mathnet  mathscinet  zmath  elib
    4. V. A. Malyshev, “Gibbs and quantum discrete spaces”, Russian Math. Surveys, 56:5 (2001), 917–972  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Kownacki J.-P., “Freezing of triangulations”, European Phys. J. B, 38:3 (2004), 485–494  crossref  adsnasa  isi  scopus  scopus
    6. Collet, P, “Dynamics of triangulations”, Journal of Statistical Physics, 121:5–6 (2005), 1073  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Eckmann, JP, “A topological glass”, Journal of Statistical Physics, 129:2 (2007), 289  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Eckmann J.-P., Procaccia I., “Ergodicity and slowing down in glass-forming systems with soft potentials: no finite-temperature singularities”, Phys. Rev. E (3), 78:1 (2008), 011503, 10 pp.  crossref  mathscinet  adsnasa  isi  scopus
    9. Ryabov G.G., “Markovskie protsessy v dinamike primitivnykh triangulyatsii v prostranstvakh $R^3$$R^4$”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 10:1 (2009), 1–8  mathnet  mathscinet  elib
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:371
    Full text:164
    References:37
    First page:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019