相关论文: Artin-Schreier L-functions and Random Unitary Matr…

We investigate the linear statistics of random matrices with purely imaginary Bernoulli entries of the form $H_{pq} = \overline{H}_{qp} = \pm i$, that are either independently distributed or exhibit global correlations imposed by the…

We study $k$-point correlators of characteristic polynomials in non-Hermitian ensembles of random matrices, focusing on the real, complex and quaternion $N \times N$ Ginibre ensembles. Our approach is based on the technique of character…

We study the joint probability density of the eigenvalues of a product of rectangular real, complex or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only…

Random matrices formed from i.i.d. standard real Gaussian entries have the feature that the expected number of real eigenvalues is non-zero. This property persists for products of such matrices, independently chosen, and moreover it is…

In a recent article we have discussed the connections between averages of powers of Riemann's $\zeta$-function on the critical line, and averages of characteristic polynomials of random matrices. The result for random matrices was shown to…

Let M be an imaginary quadratic field, f a Hecke eigenform on GL2(Q) and \pi the unitary base-change to M of the automorphic representation associated to f. Take a unitary arithmetic Hecke character \chi of M inducing the inverse of the…

Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary…

We study the eigenvectors and eigenvalues of random matrices with iid entries. Let $N$ be a random matrix with iid entries which have symmetric distribution. For each unit eigenvector $\mathbf{v}$ of $N$ our main results provide a small…

We obtain in closed form averages of polynomials, taken over hermitian matrices with the Gaussian measure involved in the Kontsevich integral, and prove a conjecture of Witten enabling one to express analogous averages with the full (cubic…

In this paper, we study the value-distributions of $L$-functions of holomorphic primitive cusp forms in the level aspect. We associate such automorphic $L$-functions with probabilistic models called the random Euler products. First, we…

In this paper, using techniques developed in our earlier works on the theory of mod-Gaussian convergence, we prove precise moderate and large deviation results for the logarithm of the characteristic polynomial of a random unitary matrix.…

For fixed $l,m \ge 1$, let $\mathbf{X}_n^{(0)},\mathbf{X}_n^{(1)},\dots,\mathbf{X}_n^{(l)}$ be independent random $n \times n$ matrices with independent entries, let $\mathbf{F}_n^{(0)} := \mathbf{X}_n^{(0)} (\mathbf{X}_n^{(1)})^{-1} \cdots…

Let $U\in U(N)$ be a random unitary matrix of size $N$, distributed with respect to the Haar measure on $U(N)$. Let $P(z)=P_U(z)$ be the characteristic polynomial of $U$. We prove that for $z$ close to the unit circle, $ \frac{P'}{P}(z) $…

We present new explicit upper bounds for the smoothness of the distribution of the random diagonal sum $S_n=\sum_{j=1}^nX_{j,\pi(j)}$ of a random $n\times n$ matrix $X=(X_{j,r})$, where the $X_{j,r}$ are independent integer valued random…

In the first part we study critical points of random polynomials. We choose two deterministic sequences of complex numbers,whose empirical measures converge to the same probability measure in complex plane. We make a sequence of polynomials…

Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to…

In this article, we study the density conjecture of Katz and Sarnak for $L$-functions of ad\'elic Hilbert modular forms and their convolutions. In particular, under the generalised Riemann hypothesis, we establish several instances…

We show the equality of the local Asai L-functions defined via the Rankin-Selberg method and the Langlands-Shahidi method for a square integrable representation of GL(n,E). As a consequence we characterise reducibility of certain induced…

Inspired by the recent works of Srivastava et al. (2010), Frasin and Aouf (2011), and Caglar et al. (2013), we introduce and investigate in the present paper two new general subclasses of the class consisting of normalized analytic and…

We consider the adjacency matrices of sparse random graphs from the Chung-Lu model, where edges are added independently between the $N$ vertices with varying probabilities $p_{ij}$. The rank of the matrix $(p_{ij})$ is some fixed positive…