Proof of the BMV conjecture
By Herbert Stahl. 2011
60 citations recorded by the source corpus.
We prove the BMV (Bessis, Moussa, Villani, [1]) conjecture, which states that the function $${t \mapsto \mathop{\rm Tr}\exp(A-tB)}$$t↦Trexp(A-tB) , $${t \geqslant 0}$$t⩾0 , is the Laplace transform of a positive measure on [0,∞) if A and B are $${n \times n}$$n×n Hermitian matrices and B is positive semidefinite. A semi-explicit representation for this measure is given.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/6f99e9efe09c517a7fe44c3c2efafd6dd2dc5e87
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Hyperbolicity and stable polynomials in combinatorics and probability (2012, result): “ant term. Let amn be the Taylor coefficients of (∂p/∂x)/p. The BMV conjecture is equivalent to the proposition that (−1)m+na mn ≥ 0 for all m,n. In July, 2011, a proof of the BMV conjecture by H. Stahl [Sta11] was posted on arXiv. At the time of writing, the refereed publication has not appeared, but ”