Witten Laplacian on a lattice spin system
From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. 115-129. 
@incollection{AST_2009__327__115_0,
     author = {Shigekawa, Ichiro},
     title = {Witten {Laplacian} on a lattice spin system},
     booktitle = {From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut},
     editor = {Dai Xianzhe and L\'eandre R\'emi and Xiaonan Ma and Zhang Weiping},
     series = {Ast\'erisque},
     pages = {115--129},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {327},
     year = {2009},
     mrnumber = {2642359},
     zbl = {1217.82022},
     language = {en},
     url = {http://www.numdam.org/item/AST_2009__327__115_0/}
}
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Shigekawa, Ichiro. Witten Laplacian on a lattice spin system, dans From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. 115-129. http://www.numdam.org/item/AST_2009__327__115_0/

[1] S. Albeverio, A. Daletskii & Y. Kondratiev - "Stochastic analysis on product manifolds: Dirichlet operators on differential forms", J. Funct. Anal. 176 (2000), p. 280- 316. | DOI | MR | Zbl

[2] P. R. Chernoff - "Schrödinger and Dirac operators with singular potentials and hyperbolic equations", Pacific J. Math. 72 (1977), p. 361-382. | DOI | MR | Zbl

[3] H. L. Cycon, R. G. Froese, W. Kirsch & B. Simon - Schrödinger operators with application to quantum mechanics and global geometry, study ed., Texts and Monographs in Physics, Springer, 1987. | MR | Zbl

[4] K. D. Elworthy & S. Rosenberg - "The Witten Laplacian on negatively curved simply connected manifolds", Tokyo J. Math. 16 (1993), p. 513-524. | DOI | MR | Zbl

[5] B. Helffer - "Remarks on decay of correlations and Witten Laplacians, Brascamp-Lieb inequalities and semiclassical limit", J. Funct. Anal. 155 (1998), p. 571-586. | DOI | MR | Zbl

[6] B. Helffer, "Remarks on decay of correlations and Witten Laplacians. II. Analysis of the dependence on the interaction", Rev. Math. Phys. 11 (1999), p. 321-336. | DOI | MR | Zbl

[7] B. Helffer, "Remarks on decay of correlations and Witten Laplacians. III. Application to logarithmic Sobolev inequalities", Ann. Inst. H. Poincaré Probab. Statist. 35 (1999), p. 483-508. | DOI | EuDML | Numdam | MR | Zbl

[8] B. Helffer, Semiclassical analysis, Witten Laplacians, and statistical mechanics, Series in Partial Differential Equations and Applications, vol. 1, World Scientific Publishing Co. Inc., 2002. | DOI | MR | Zbl

[9] O. Matte & J. S. Møller - "On the spectrum of semi-classical Witten-Laplacians and Schrödinger operators in large dimension", J. Funct. Anal. 220 (2005), p. 243-264. | DOI | MR | Zbl

[10] N. Yoshida - "The log-Sobolev inequality for weakly coupled lattice fields", Probab. Theory Related Fields 115 (1999), p. 1-40. | DOI | MR | Zbl

[11] B. Zegarlinski - "The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice", Comm. Math. Phys. 175 (1996), p. 401-432. | DOI | MR | Zbl