Fonction de Correlation pour des Mesures Complexes
Wang, Wei Min1
1 Dépt. de Mathématiques, Université de Paris Sud, F-91405 Orsay cedex and URA 760, CNRS
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 20, 8 p.

We study a class of holomorphic complex measures, which are close in an appropriate sense to a complex Gaussian. We show that these measures can be reduced to a product measure of real Gaussians with the aid of a maximum principle in the complex domain. The formulation of this problem has its origin in the study of a certain class of random Schrödinger operators, for which we show that the expectation value of the Green’s function decays exponentially.

Wang, Wei Min 1

1 Dépt. de Mathématiques, Université de Paris Sud, F-91405 Orsay cedex and URA 760, CNRS 
@article{SEDP_1998-1999____A20_0,
     author = {Wang, Wei Min},
     title = {Fonction de {Correlation} pour des {Mesures} {Complexes}},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:20},
     pages = {1--8},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {1998-1999},
     zbl = {1086.82538},
     language = {en},
     url = {http://archive.numdam.org/item/SEDP_1998-1999____A20_0/}
}
TY  - JOUR
AU  - Wang, Wei Min
TI  - Fonction de Correlation pour des Mesures Complexes
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:20
PY  - 1998-1999
SP  - 1
EP  - 8
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://archive.numdam.org/item/SEDP_1998-1999____A20_0/
LA  - en
ID  - SEDP_1998-1999____A20_0
ER  - 
%0 Journal Article
%A Wang, Wei Min
%T Fonction de Correlation pour des Mesures Complexes
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:20
%D 1998-1999
%P 1-8
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://archive.numdam.org/item/SEDP_1998-1999____A20_0/
%G en
%F SEDP_1998-1999____A20_0
Wang, Wei Min. Fonction de Correlation pour des Mesures Complexes. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 20, 8 p. http://archive.numdam.org/item/SEDP_1998-1999____A20_0/

[A] P. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109, 1492 (1958).

[AM] M. Aizenman and S. Molchanov, Localization at large disorder and at extreme energies: an elementary derivation, Commun. Math. Phys. 157, 245 (1993). | MR | Zbl

[Be] F. A. Berezin, The method of second quantization, New York: Academic press, 1966. | MR | Zbl

[BCKP] A. Bovier, M. Campanino, A. Klein, and F. Perez, Smoothness of the density of states in the Anderson model at high disorder, Commun. Math. Phys. 114 439-461, (1988). | MR | Zbl

[CFS] F. Constantinescu, J. Fröhlich, and T. Spencer, Analyticity of the density of states and replica method for random Schrödinger operators on a lattice, J. Stat. Phys. 34 571-596, (1984). | MR | Zbl

[DK] H. von Dreifus and A. Klein, A new proof of localization in the Anderson tight binding model, Commun. Math. Phys. 124, 285-299 (1989). | MR | Zbl

[Ec] E. N. Economu, Green’s functions in quantum physics, Springer Series in Solid State Sciences 7, 1979.

[FMSS] J. Fröhlich, F. Martinelli, E. Scoppola and T.Spencer, Constructive proof of localization in Anderson tight binding model, Commun. Math. Phys. 101, 21-46 (1985). | MR | Zbl

[FS] J. Fröhlich and T.Spencer, Absence of diffusion in the Anderson tight binding model for large disorder or low energy, Commun. Math. Phys. 88, 151-184 (1983). | MR | Zbl

[HS] B. Helffer and J. Sjöstrand, On the correlation for Kac-like models in the convex case, J. of Stat. Phys. (1994). | MR | Zbl

[K] A. Klein, The supersymmetric replica trick and smoothness of the density of states for the random Schrödinger operators, Proceedings of Symposium in Pure Mathematics, 51, 1990. | MR | Zbl

[KS] A. Klein and A. Spies, Smoothness of the density of states in the Anderson model on a one dimensional strip, Ann. of Phys. 183, 352-398 (1988). | MR | Zbl

[S1] J. Sjöstrand, Ferromagnetic integrals, correlations and maximum principle, Ann. Inst. Fourier 44, 601-628 (1994). | Numdam | MR | Zbl

[S2] J. Sjöstrand, Correlation asymptotics and Witten Laplacians, Algebra and Analysis 8 (1996). | MR | Zbl

[SW1] J. Sjöstrand and W. M. Wang, Supersymmetric measures and maximum principles in the complex domaine– exponential decay of Green’s functions, Ann. Scient. Ec. Norm. Sup. 32, (1999). | Numdam | Zbl

[SW2] J. Sjöstrand and W. M. Wang, Exponential decay of averaged Green functions for the random Schrödinger operators, a direct approach, Ann. Scient. Ec. Norm. Sup. 32, (1999) . | Numdam | MR | Zbl

[Sp] T. Spencer, The Schrödinger equation with a random potential–a mathematical review, Les Houches XLIII, K. Osterwalder, R. Stora (eds.) (1984). | Zbl

[V] T. Voronov, Geometric integration theory on supermanifolds, Mathematical Physics Review, USSR Academy of Sciences, Moscow, 1993.

[W1] W. M. Wang, Asymptotic expansion for the density of states of the magnetic Schrödinger operator with a random potential, Commun. Math. Phys. 172, 401-425 (1995). | MR | Zbl

[W2] W. M. Wang, Supersymmetry and density of states of the magnetic Schrödinger operator with a random potential revisited, Commun. PDE (1999). | MR | Zbl