Loading [MathJax]/jax/output/SVG/config.js
Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






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


Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 159, Number 1, Pages 34–57
DOI: https://doi.org/10.4213/tmf6331
(Mi tmf6331)
 

This article is cited in 19 scientific papers (total in 20 papers)

Global eigenvalue distribution regime of random matrices with an anharmonic potential and an external source

A. I. Aptekarev, V. G. Lysov, D. N. Tulyakov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
References:
Abstract: We consider ensembles of random Hermitian matrices with a distribution measure determined by a polynomial potential perturbed by an external source. We find the genus-zero algebraic function describing the limit mean density of eigenvalues in the case of an anharmonic potential and a diagonal external source with two symmetric eigenvalues. We discuss critical regimes where the density support changes the connectivity or increases the genus of the algebraic function and consequently obtain local universal asymptotic representations for the density at interior and boundary points of its support (in the generic cases). The investigation technique is based on an analysis of the asymptotic properties of multiple orthogonal polynomials, equilibrium problems for vector potentials with interaction matrices and external fields, and the matrix Riemann–Hilbert boundary value problem.
Keywords: random matrix, matrix model, eigenvalue distribution, Brownian bridge, multiple orthogonal polynomial.
Received: 07.07.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 1, Pages 448–468
DOI: https://doi.org/10.1007/s11232-009-0036-0
Bibliographic databases:
Language: Russian
Citation: A. I. Aptekarev, V. G. Lysov, D. N. Tulyakov, “Global eigenvalue distribution regime of random matrices with an anharmonic potential and an external source”, TMF, 159:1 (2009), 34–57; Theoret. and Math. Phys., 159:1 (2009), 448–468
Citation in format AMSBIB
\Bibitem{AptLysTul09}
\by A.~I.~Aptekarev, V.~G.~Lysov, D.~N.~Tulyakov
\paper Global eigenvalue distribution regime of random matrices with an~anharmonic potential and an~external source
\jour TMF
\yr 2009
\vol 159
\issue 1
\pages 34--57
\mathnet{http://mi.mathnet.ru/tmf6331}
\crossref{https://doi.org/10.4213/tmf6331}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2547435}
\zmath{https://zbmath.org/?q=an:1180.82071}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2009TMP...159..448A}
\elib{https://elibrary.ru/item.asp?id=15304501}
\transl
\jour Theoret. and Math. Phys.
\yr 2009
\vol 159
\issue 1
\pages 448--468
\crossref{https://doi.org/10.1007/s11232-009-0036-0}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000269080400002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70349540673}
Linking options:
  • https://www.mathnet.ru/eng/tmf6331
  • https://doi.org/10.4213/tmf6331
  • https://www.mathnet.ru/eng/tmf/v159/i1/p34
  • This publication is cited in the following 20 articles:
    1. A.V. Tsvetkova, “Real Semiclassical Approximation for the Asymptotics of Jacobi Polynomials Given by a Difference Equation”, Russ. J. Math. Phys., 31:4 (2024), 774  crossref
    2. Martinez-Finkelshtein A., Silva G.L.F., “Spectral Curves, Variational Problems and the Hermitian Matrix Model With External Source”, Commun. Math. Phys., 383:3 (2021), 2163–2242  crossref  mathscinet  isi
    3. Martinez-Finkelshtein A., Silva G.L.F., “Critical Measures For Vector Energy: Asymptotics of Non-Diagonal Multiple Orthogonal Polynomials For a Cubic Weight”, Adv. Math., 349 (2019), 246–315  crossref  mathscinet  isi
    4. M. A. Lapik, D. N. Tulyakov, “On expanding neighborhoods of local universality of Gaussian unitary ensembles”, Proc. Steklov Inst. Math., 301 (2018), 170–179  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. M. V. Sidortsov, N. A. Starovoitova, A. P. Starovoitov, “Ob asimptotike approksimatsii Ermita–Pade vtorogo roda dlya eksponentsialnykh funktsii s kompleksnymi mnozhitelyami v pokazatelyakh eksponent”, PFMT, 2017, no. 1(30), 73–77  mathnet
    6. A. P. Starovoitov, “Asymptotics of Diagonal Hermite–Padé Polynomials for the Collection of Exponential Functions”, Math. Notes, 102:2 (2017), 277–288  mathnet  crossref  crossref  mathscinet  isi  elib
    7. A. P. Starovoitov, E. P. Kechko, “On Some Properties of Hermite–Padé Approximants to an Exponential System”, Proc. Steklov Inst. Math., 298 (2017), 317–333  mathnet  crossref  crossref  isi  elib
    8. M. A. Lapik, D. N. Tulyakov, “Raspredelenie nulei mnogochlenov Ermita vblizi nulya i gaussovskie unitarnye ansambli”, Preprinty IPM im. M. V. Keldysha, 2017, 129, 11 pp.  mathnet  crossref
    9. A. P. Starovoitov, E. P. Kechko, “Upper Bounds for the Moduli of Zeros of Hermite–Padé Approximations for a Set of Exponential Functions”, Math. Notes, 99:3 (2016), 417–425  mathnet  crossref  crossref  mathscinet  isi  elib
    10. A. P. Starovoitov, G. N. Kazimirov, M. V. Sidortsov, “Asimptotika approksimatsii Ermita–Pade eksponentsialnykh funktsii s kompleksnymi mnozhitelyami v pokazatelyakh eksponent”, PFMT, 2016, no. 2(27), 61–67  mathnet
    11. A. P. Starovoitov, E. P. Kechko, “O lokalizatsii nulei approksimatsii Ermita–Pade eksponentsialnykh funktsii”, PFMT, 2015, no. 3(24), 84–89  mathnet
    12. V. M. Buchstaber, V. N. Dubinin, V. A. Kaliaguine, B. S. Kashin, V. N. Sorokin, S. P. Suetin, D. N. Tulyakov, B. N. Chetverushkin, E. M. Chirka, A. A. Shkalikov, “Alexander Ivanovich Aptekarev (on his 60th birthday)”, Russian Math. Surveys, 70:5 (2015), 965–973  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. M. A. Lapik, “Ekstremalnyi funktsional dlya vektornykh zadach ravnovesiya logarifmicheskogo potentsiala vo vneshnem pole s matritsei vzaimodeistviya Anzhelesko”, Preprinty IPM im. M. V. Keldysha, 2015, 083, 23 pp.  mathnet
    14. A. P. Starovoitov, “On asymptotic form of the Hermite–Pade approximations for a system of Mittag-Leffler functions”, Russian Math. (Iz. VUZ), 58:9 (2014), 49–56  mathnet  crossref
    15. A. P. Starovoitov, “Approksimatsii Ermita–Pade dlya sistemy funktsii Mittag-Lefflera”, PFMT, 2013, no. 1(14), 81–87  mathnet
    16. A. I. Aptekarev, V. G. Lysov, D. N. Tulyakov, “Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials”, Sb. Math., 202:2 (2011), 155–206  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. Bleher P., Delvaux S., Kuijlaars A.B.J., “Random matrix model with external source and a constrained vector equilibrium problem”, Comm. Pure Appl. Math., 64:1 (2011), 116–160  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    18. A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. A. I. Aptekarev, A. Kuijlaars, “Hermite–Padé approximations and multiple orthogonal polynomial ensembles”, Russian Math. Surveys, 66:6 (2011), 1133–1199  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    20. A. I. Aptekarev, V. G. Lysov, “Systems of Markov functions generated by graphs and the asymptotics of their Hermite-Padé approximants”, Sb. Math., 201:2 (2010), 183–234  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:827
    Full-text PDF :280
    References:70
    First page:19
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025