Related papers: Proof of the BMV Conjecture

The Shimura-Taniyama conjecture states that the Mellin transform of the Hasse-Weil L-function of any elliptic curve defined over the rational numbers is a modular form. Recent work of Wiles, Taylor-Wiles and Breuil-Conrad-Diamond-Taylor has…

Consider a mixing dynamical systems $([0,1], T, \mu)$, for instance a piecewise expanding interval map with a Gibbs measure $\mu$. Given a non-summable sequence $(m_k)$ of non-negative numbers, one may define $r_k (x)$ such that $\mu (B(x,…

Let $(X, \mathscr{L}, \lambda)$ and $(Y, \mathscr{M}, \mu)$ be finite measure spaces for which there exist $A \in \mathscr{L}$ and $B \in \mathscr{M}$ with either $0 < \lambda(A) < 1 < \lambda(X)$ and $0 < \mu(B) < \mu(Y)$, or the other way…

In this paper, we present an elementary proof of the Bhatia-\v{S}emrl Theorem, utilizing the Minimax Theorem for bounded linear operators by Asplund and Ptak [1]. Some related results are also discussed.

Let $G = (V,E)$ be a connected graph. A probability measure $\mu$ on $V$ is called "balanced" if it has the following property: if $T_\mu(v)$ denotes the "earth mover's" cost of transporting all the mass of $\mu$ from all over the graph to…

Let $\mathcal{L}\{f(t)\} = \int_{0}^{\infty}e^{-st}f(t)dt$ denote the Laplace transform of $f$. It is well-known that if $f(t)$ is a piecewise continuous function on the interval $t:[0,\infty)$ and of exponential order for $t > N$; then…

In this paper, we prove a quantitative version of the Oppenheim conjecture for indefinite ternary quadratic forms: for any indefinite irrational ternary quadratic form $Q$ that is not extremely well approxiable by rational forms, and for…

We give a formula that represents magnetic Berezin transforms associated with generalized Bergman spaces as functions of the Laplace-Beltrami operator on the Bergman ball. In particular, we recover the result obtained by J. Peeter [J. Oper.…

A Bernstein-von Mises theorem is derived for general semiparametric functionals. The result is applied to a variety of semiparametric problems in i.i.d. and non-i.i.d. situations. In particular, new tools are developed to handle…

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

In this paper we prove a conjecture regarding the form of the Born-Infeld Lagrangian with a U(1)^2n gauge group after the elimination of the auxiliary fields. We show that the Lagrangian can be written as a symmetrized trace of Lorentz…

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…

We analyse the $B \rightarrow \tau \nu$ decay in a generic two-Higgs doublet model satisfying the MFV hypothesis. In particular, we analyse under which conditions $\BR(B \rightarrow \tau \nu)$ can be substantially enhanced over its SM…

Let $\xi$ be a L\'{e}vy process and $I_\xi(t):=\int_{0}^te^{-\xi_s}\mathrm{d} s$, $t\geq 0,$ be the exponential functional of L\'{e}vy processes on deterministic horizon. Given that $\lim_{t\to \infty}\xi_t=-\infty$ we evaluate for general…

This paper is concerned with the structure of the set of Riemannian metrics on a connected manifold such that the corresponding Laplace--Beltrami operator has an eigenvalue of a given multiplicity. The starting point of our investigation is…

The Bernstein Markov Property, shortly BMP, is an asymptotic quan- titative assumption on the growth of uniform norms of polynomials or rational functions on a compact set with respect to L {\mu} 2 -norms, where {\mu} is a positive finite…

The classical Perron-Frobenius theory asserts that for two matrices $A$ and $B$, if $0\leq B \leq A$ and $r(A)=r(B)$ with $A$ being irreducible, then $A=B$. This was recently extended in Bernik et al. (2012) to positive operators on…

We consider a process $(X_t)_{t\in[0,T)}$ given by the SDE $dX_t = \alpha b(t)X_t dt + \sigma(t) dB_t$, $t\in[0,T)$, with initial condition $X_0=0$, where $T\in(0,\infty]$, $\alpha\in R$, $(B_t)_{t\in[0,T)}$ is a standard Wiener process,…

For a large class of symplectic integer matrices, the action on the torus extends to a symplectic $\mathbb{Z}^r$-action with $r\geq 2$. We apply this to the study of semiclassical measures for joint eigenfunctions of the quantization of the…

In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weaker form of this inequality [2].