相关论文: Further implications of the Bessis-Moussa-Villani …

We prove the BMV (Bessis, Moussa, Villani, 1975) conjecture, which states that the function t -> Tr exp(A-tB), t \geq 0, is the Laplace transform of a positive measure on [0,\infty) if A and B are n x n Hermitian matrices and B is positive…

The BMV conjecture for traces, which states that $Tr exp(A -\lambda B)$ is the Laplace transform of a positive measure, is shown to be equivalent to two other statements: (i) The polynomial $\lambda\mapsto Tr(A+\lambda B)^p$ has only…

The Bessis-Moussa-Villani conjecture states that the trace of $\exp(A-tB)$ is, as a function of the real variable $t$, the Laplace transform of a positive measure, where $A$ and $B$ are respectively a hermitian and positive semi-definite…

We study trace functions on the form $ t\to\tr f(A+tB) $ where $ f $ is a real function defined on the positive half-line, and $ A $ and $ B $ are matrices such that $ A $ is positive definite and $ B $ is positive semi-definite. If $ f $…

The BMV conjecture states that for \(n\times n\) Hermitian matrices \(A\) and \(B\) the function \(f_{A,B}(t)=\tr e^{tA+B}\) is exponentially convex. Recently the BMV conjecture was proved by Herbert Stahl. The proof of Herbert Stahl is…

The BMV conjecture states that for $n\times n$ Hermitian matrices $A$ and $B$ the function $f_{A,B}(t)=trace{\, } e^{tA+B}$ is exponentially convex. Recently the BMV conjecture was proved by Herbert Stahl. The proof of Herbert Stahl is…

Consider the polynomial $tr (A + tB)^m$ in $t$ for positive hermitian matrices $A$ and $B$ with $m \in \N$. The Bessis-Moussa-Villani conjecture (in the equivalent form of Lieb and Seiringer) states that this polynomial has nonnegative…

We obtain a solution to the Bessis-Moussa-Villani conjecture for a trace-class perturbation of a semi-bounded operator and answer affirmatively the question on positivity of higher order spectral shift functions in the setting of…

Consider the polynomial $tr (A + tB)^m$ in $t$ for positive hermitian matrices $A$ and $B$ with $m \in \N$. The Bessis-Moussa-Villani conjecture (in the equivalent form of Lieb and Seiringer) states that this polynomial has nonnegative…

Given a pair $A,B$ of matrices of size $n\times n$, we consider the matrix function $e^{At+B}$ of the variable $t\in\mathbb{C}$. If the matrix $A$ is Hermitian, the matrix function $e^{At+B}$ is representable as the bilateral Laplace…

The 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 Hermitean A and B.

We show that for fixed $A,B$, hermitian nonnegative definite matrices, and fixed $k$ the coefficients of the $t^k$ in the polynomial $\tr (A+tB)^m$ is positive if $\tr AB >0$ and $m>N(A,B,k)$.

In this article, a model of random hermitian matrices is considered, in which the measure $\exp(-S)$ contains a general U(N)-invariant potential and an external source term: $S=N\tr(V(M)+MA)$. The generalization of known determinant…

In this paper we derive the Laplace transforms of the integral functionals $$ \int_0^\infty (p(\exp(B^{(\mu)}_t)+1)^{-1}+ q(\exp(B^{(\mu)}_t)+1)^{-2}) dt, $$ $$ \int_0^\infty (p(\exp(R^{(3)}_t)-1)^{-1}+ q(\exp(R^{(3)}_t)-1)^{-2}) dt, $$…

The Bessis-Moussa-Villani (BMV) conjecture, originating in quantum statistical mechanics, was proved by Stahl after an influential reformulation by Lieb and Seiringer. A later refinement asks whether the normalized average over all words…

It is shown that the polynomial $\lambda(t) = {\rm Tr}[(A + tB)^p]$ has nonnegative coefficients when $p \leq 7$ and A and B are any two complex positive semidefinite $n \times n$ matrices with arbitrary $n$. This proofs a general…

The reformulation of the Bessis-Moussa-Villani conjecture given by Lieb and Seiringer asserts that the coefficient of t^r in the polynomial Trace[(A+tB)^p], with A and B positive semidefinite matrices, is nonnegative for all p and r. We…

For two hermitian matrices $A$ and $B$, Golden-Thompson inequality \cite{golden1965lower, thompson1965inequality} states that $$ \mathrm{tr}\left[ \exp{(A+B)} \right] \leq \mathrm{tr}\left[ \exp{(A)}\exp{(B)} \right]. $$ We elaborate here…

In this short note we reduce the b-semiampleness conjecture for lc-trivial fibrations to the b-semiampleness conjecture for klt-trivial fibrations.

We demonstrate three properties conjectured to hold for a certain function by Levin (2025) in a study of the blimpy graphical shape of the number of bit strings with a given score under an interesting scoring system. The properties include…