Infinite volume asymptotics of the ground state energy in a scaled poissonian potential

Franz Merkl; Mario V. Wüthrich

Annales de l'I.H.P. Probabilités et statistiques (2002)

  • Volume: 38, Issue: 3, page 253-284
  • ISSN: 0246-0203

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Merkl, Franz, and Wüthrich, Mario V.. "Infinite volume asymptotics of the ground state energy in a scaled poissonian potential." Annales de l'I.H.P. Probabilités et statistiques 38.3 (2002): 253-284. <http://eudml.org/doc/77716>.

@article{Merkl2002,
author = {Merkl, Franz, Wüthrich, Mario V.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random Schrödinger operator; ground state energy},
language = {eng},
number = {3},
pages = {253-284},
publisher = {Elsevier},
title = {Infinite volume asymptotics of the ground state energy in a scaled poissonian potential},
url = {http://eudml.org/doc/77716},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Merkl, Franz
AU - Wüthrich, Mario V.
TI - Infinite volume asymptotics of the ground state energy in a scaled poissonian potential
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 3
SP - 253
EP - 284
LA - eng
KW - random Schrödinger operator; ground state energy
UR - http://eudml.org/doc/77716
ER -

References

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  1. [1] M. Abramowitz, A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York, 1972. 
  2. [2] M. van den Berg, E. Bolthausen, F. den Hollander, Moderate deviations for the volume of the Wiener sausage, Annals of Mathematics153 (2) (2001) 355-406. Zbl1004.60021MR1829754
  3. [3] E.H. Lieb, M. Loss, Analysis, in: Graduate Studies in Mathematics, 14, American Mathematical Society, RI, 1997. Zbl0873.26002MR1415616
  4. [4] F. Merkl, M.V. Wüthrich, Phase transition of the principal Dirichlet eigenvalue in a scaled Poissonian potential, Probab. Theory Related Fields119 (4) (2001) 475-507. Zbl1037.82022MR1826404
  5. [5] M. Reed, B. Simon, Methods of Modern Mathematical Physics II: Fourier Analysis, Self Adjointness, Academic Press, San Diego, 1975. Zbl0308.47002MR493420
  6. [6] M. Reed, B. Simon, Methods of Modern Mathematical Physics IV: Analysis of Operators, Academic Press, San Diego, 1978. Zbl0401.47001MR493421
  7. [7] B. Simon, Functional Integration and Quantum Physics, Academic Press, New York, 1979. Zbl0434.28013MR544188
  8. [8] A.S. Sznitman, Shape theorem, Lyapounov exponents and large deviations for Brownian motion in a Poissonian potential, Comm. Pure. Appl. Math.47 (12) (1994) 1655-1688. Zbl0814.60022MR1303223
  9. [9] A.S. Sznitman, Brownian Motion, Obstacles and Random Media, Springer, Berlin, 1998. Zbl0973.60003MR1717054
  10. [10] G.N. Watson, A Treatise on the Theory of Bessel Functions, in: Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996, reprinted. Zbl0849.33001MR1349110

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