RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
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


TMF, 2018, Volume 195, Number 2, Pages 171–189 (Mi tmf9405)  

Functional integrals for the Bogoliubov Gaussian measure: Exact asymptotic forms

V. R. Fatalov

Lomonosov Moscow State University, Moscow, Russia

Abstract: We prove theorems on the exact asymptotic forms as $u\to\infty$ of two functional integrals over the Bogoliubov measure $\mu_{{\mathrm B}}$ of the forms
$$ \int_{C[0,\beta]}[ \int_0^\beta |x(t)|^p dt]^{u} d\mu_{{\mathrm B}}(x),\qquad \int_{C[0,\beta]}\exp\{u( \int_0^\beta |x(t)|^p dt)^{\alpha/p} \} d\mu_{{\mathrm B}}(x) $$
for $p=4,6,8,10$ with $p>p_0$, where $p_0=2+4\pi^2/\beta^2\omega^2$ is the threshold value, $\beta$ is the inverse temperature, $\omega$ is the eigenfrequency of the harmonic oscillator, and $0<\alpha<2$. As the method of study, we use the Laplace method in Hilbert functional spaces for distributions of almost surely continuous Gaussian processes.

Keywords: Bogoliubov measure, almost surely continuous Gaussian process, Laplace method in a functional Hilbert space, manifold of minimum values.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00050
This work was supported by the Russian Foundation for Basic Research (Grant No. 11-01-00050).


DOI: https://doi.org/10.4213/tmf9405

Full text: PDF file (546 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2018, 195:2, 641–657

Bibliographic databases:

Document Type: Article
Received: 24.05.2017
Revised: 24.08.2017

Citation: V. R. Fatalov, “Functional integrals for the Bogoliubov Gaussian measure: Exact asymptotic forms”, TMF, 195:2 (2018), 171–189; Theoret. and Math. Phys., 195:2 (2018), 641–657

Citation in format AMSBIB
\Bibitem{Fat18}
\by V.~R.~Fatalov
\paper Functional integrals for the~Bogoliubov Gaussian measure: Exact asymptotic forms
\jour TMF
\yr 2018
\vol 195
\issue 2
\pages 171--189
\mathnet{http://mi.mathnet.ru/tmf9405}
\crossref{https://doi.org/10.4213/tmf9405}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018TMP...195..641F}
\elib{http://elibrary.ru/item.asp?id=32823067}
\transl
\jour Theoret. and Math. Phys.
\yr 2018
\vol 195
\issue 2
\pages 641--657
\crossref{https://doi.org/10.1134/S004057791805001X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000434491300001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048293982}


Linking options:
  • http://mi.mathnet.ru/eng/tmf9405
  • https://doi.org/10.4213/tmf9405
  • http://mi.mathnet.ru/eng/tmf/v195/i2/p171

    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
  • Number of views:
    This page:88
    References:9
    First page:13

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