Ferromagnetic integrals, correlations and maximum principles

Johannes Sjöstrand

Annales de l'institut Fourier (1994)

  • Volume: 44, Issue: 2, page 601-628
  • ISSN: 0373-0956

Abstract

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For correlations of the form (0.2) we consider a critical case and prove power decay upper bounds in terms of the fundamental solution of a certain elliptic operator. This is achieved by improving the use of a maximum principle. We also formulate a general maximum principle and give two applications.

How to cite

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Sjöstrand, Johannes. "Ferromagnetic integrals, correlations and maximum principles." Annales de l'institut Fourier 44.2 (1994): 601-628. <http://eudml.org/doc/75075>.

@article{Sjöstrand1994,
abstract = {For correlations of the form (0.2) we consider a critical case and prove power decay upper bounds in terms of the fundamental solution of a certain elliptic operator. This is achieved by improving the use of a maximum principle. We also formulate a general maximum principle and give two applications.},
author = {Sjöstrand, Johannes},
journal = {Annales de l'institut Fourier},
keywords = {exponential convergence of the first eigenvalue; expectation values; maximum principle},
language = {eng},
number = {2},
pages = {601-628},
publisher = {Association des Annales de l'Institut Fourier},
title = {Ferromagnetic integrals, correlations and maximum principles},
url = {http://eudml.org/doc/75075},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Sjöstrand, Johannes
TI - Ferromagnetic integrals, correlations and maximum principles
JO - Annales de l'institut Fourier
PY - 1994
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 2
SP - 601
EP - 628
AB - For correlations of the form (0.2) we consider a critical case and prove power decay upper bounds in terms of the fundamental solution of a certain elliptic operator. This is achieved by improving the use of a maximum principle. We also formulate a general maximum principle and give two applications.
LA - eng
KW - exponential convergence of the first eigenvalue; expectation values; maximum principle
UR - http://eudml.org/doc/75075
ER -

References

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  1. [BL]H.J. BRASCAMP, E.H. LIEB, On extensions of the Brunn-Minkovski and Prékopa Leindler theorems,..., J. Funct. An., 22 (1976), 366-389. Zbl0334.26009
  2. [BrFLeSp]J. BRICMONT, J.R. FONTAINE, J.L. LEBOWITZ, T. SPENCER, Lattice systems with continuous symmetry II. Decay of correlations, Comm. Math. Phys., 78 (1981), 363-373. 
  3. [BrFLeLSp]J. BRICMONT, J.R. FONTAINE, J.L. LEBOWITZ, E.H. LIEB, T. SPENCER, Lattice systems with continuous symmetry III. Low temperature asymptotic expansion for the plane rotator model, Comm. Math. Phys., 78 (1981), 545-566. 
  4. [C]P. CARTIER, Inégalités de correlation en mécanique statistique, Sém. Bourbaki, 25ème année, 1972-1973, n° 431, Springer LNM n° 383. 
  5. [E]R.S. ELLIS, Entropy, large deviations and statistical mechanics, Grundlehren der Math. Wiss., 271, Springer (1985). Zbl0566.60097MR87d:82008
  6. [GlJ]J. GLIMM, A. JAFFEE, Quantum physics, a functional integral point of view, second edition, Springer (1987). 
  7. [Gr]G. GRIMMETT, Percolation, Springer (1989). Zbl0691.60089MR90j:60109
  8. [GRSi]F. GUERRA, L. ROSEN, B. SIMON, The p(ø)2 Euclidean quantum field theory as classical statistical mechanics, Ann. Math., 101 (1975), 111-259. 
  9. [HS]B. HELFFER, J. SJÖSTRAND, On the correlation for Kac like models in the convex case, report n° 9, 1992-1993, Institut Mittag-Leffler. Zbl0946.35508
  10. [SinWYY]I.M. SINGER, B. WONG, S.T. YAU, S.S.T. YAU, An estimate of the gap of the first two eigenvalues of the Schrödinger operator, Ann. Sc. Norm. Sup. Pisa (ser. 4), 12 (1985), 319-333. Zbl0603.35070MR87j:35280
  11. [S]J. SJÖSTRAND, Exponential convergence of the first eigenvalue divided by the dimension, for certain sequences of Schrödinger operators, Astérisque, 210 (1992), 303-326. Zbl0796.35123
  12. [So]A.D. SOKAL, Mean field bounds and correlation inequalities, J. Stat. Phys., 28 (1982), 431-439. 

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