Related papers: Murmurations and ratios conjectures
Higher-order gravity models have been recently the subject of much attention in the context of cosmic acceleration. These models are derived by adding various curvature invariants to the Einstein-Hilbert action. Several studies showed that…
We study the second moment of the central values of quadratic twists of a modular $L$-function. Unconditionally, we obtain a lower bound which matches the conjectured asymptotic formula, while on GRH we prove the asymptotic formula itself.
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
Recently, we have classified Hermitian random matrix ensembles that are invariant under the conjugate action of the unitary group and stable with respect to matrix addition. Apart from a scaling and a shift, the whole information of such an…
We prove precise conditional estimates for the third moment of the logarithm of the Riemann zeta function, refining what is implied by the Selberg central limit theorem, both for the real and imaginary parts. These estimates match…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
We present a unified integral framework based on the Fourier-Laplace transform evaluated along a vertical line in the complex plane. By identifying the moment-generating function (MGF) of a random variable with the weights of these…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
The diagonalization of Hermitian supermatrices is studied. Such a change of coordinates is inevitable to find certain structures in random matrix theory. However it still poses serious problems since up to now the calculation of all…
We study a new type of normal form at a critical point of an analytic Hamiltonian. Under a Bruno condition on the frequency, we prove a convergence statement to the normal form. Using this result, we prove the Herman invariant tori…
The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this…
We study coupled random walks in the plane such that, at each step, the walks change direction by a uniform random angle plus an extra deterministic angle \theta. We compute the Hausdorff dimension of the \theta for which the walk has an…
Identification-robust hypothesis tests are commonly based on the continuous updating GMM objective function. When the number of moment conditions grows proportionally with the sample size, the large-dimensional weighting matrix prohibits…
First-order perturbative calculation of the frequency-shifts caused by special relativity is performed for a charged particle confined in a Penning trap. The perturbed motion is approximated by the Jacobian elliptic functions which describe…
A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These…
We present a new combinatorial and conjectural algorithm for computing the Mullineux involution for the symmetric group and its Hecke algebra. This algorithm is built on a conjectural property of crystal isomorphisms which can be rephrased…
We show that the "twisted" planar random walk - which results by summing up stationary increments rotated by multiples of a fixed angle - is recurrent under diverse assumptions on the increment process. For example, if the increment process…
The transformations of the sum identities for generalized harmonic and oscillatory numbers, obtained earlier in our recent report [1], enable us to derive the new identities expressed in terms of the corresponding square roots of x. At…
Assuming the Riemann Hypothesis, Goldston, Gonek and Montgomery \cite{GGM} studied the second moment of the log-derivative of $\zeta$, shifted away from the half line by $a/\log T$, and its connection with the pair correlation conjecture.…
Using the standard concepts of free random variables, we show that for a large class of nonhermitean random matrix models, the support of the eigenvalue distribution follows from their hermitean analogs using a conformal transformation. We…