Geodesic
Herbert Stahl's proof of the BMV conjecture
Sbornik. Mathematics, Tome 206 (2015) no. 1, pp. 87-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper contains a simplified version of Stahl's proof of a conjecture of Bessis, Moussa and Villani on the trace of matrices $A+tB$ with Hermitian $A$ and $B$. Bibliography: 5 titles.
Keywords: perturbation theory, trace, Riemann surfaces.
Mots-clés : Hermitian matrices 
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A. E. Eremenko. Herbert Stahl's proof of the BMV conjecture. Sbornik. Mathematics, Tome 206 (2015) no. 1, pp. 87-92. http://geodesic.mathdoc.fr/item/SM_2015_206_1_a5/

[1] H. R. Stahl, “Proof of the BMV conjecture”, Acta Math., 211:2 (2013), 255–290 | DOI | MR | Zbl

[2] D. Bessis, P. Moussa, M. Villani, “Monotonic converging variational approximations to the functional integrals in quantum statistical mechanics”, J. Mathematical Phys., 16:11 (1975), 2318–2385 | DOI | MR | Zbl

[3] E. H. Lieb, R. Steiringer, “Equivalent forms of the Bessis–Moussa–Villani conjecture”, J. Statist. Phys., 115:1–2 (2004), 185–190 | DOI | MR | Zbl

[4] P. Moussa, “On the representation of $\operatorname{Tr}(e^{A-\lambda B})$ as a Laplace transform”, Rev. Math. Phys., 12:4 (2000), 621–655 | DOI | MR | Zbl

[5] M. Reed, B. Simon, Methods of mathematical physics, v. IV, Analysis of operators, Academic Press, New York–London, 1978, xv+396 pp. | MR | MR | Zbl | Zbl