Related papers: Truncations of random unitary matrices and Young t…
We give a new heuristic for all of the main terms in the integral moments of various families of primitive L-functions. The results agree with previous conjectures for the leading order terms. Our conjectures also have an almost identical…
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.
We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…
We study the eigenvalues of the covariance matrix $\frac{1}{n}M^*M$ of a large rectangular matrix $M=M_{n,p}=(\zeta_{ij})_{1\leq i\leq p;1\leq j\leq n}$ whose entries are i.i.d. random variables of mean zero, variance one, and having finite…
We investigate the properties of uniform doubly stochastic random matrices, that is non-negative matrices conditioned to have their rows and columns sum to 1. The rescaled marginal distributions are shown to converge to exponential…
We show that the maximum moments of the sum of independent positive semidefinite random matrices with given norm upper bounds and norms of expectations is attained when all the random matrices are the multiplications of certain random…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
Number theorists have studied extensively the connections between the distribution of zeros of the Riemann $\zeta$-function, and of some generalizations, with the statistics of the eigenvalues of large random matrices. It is interesting to…
The random walk to be considered takes place in the d- spherical dual of the group U(n + 1), for a fixed finite dimensional irreducible representation d of U(n). The transition matrix comes from the three term recursion relation satisfied…
The $\mathcal{A}$-tracial algebras are algebras endowed with multi-linear forms, compatible with the product, and indexed by partitions. Using the notion of $\mathcal{A}$-cumulants, we define and study the $\mathcal{A}$-freeness property…
We investigate when a linear functional $L$ defined on a linear subspace $B$ of a unital commutative real algebra $A$ admits an integral representation w.r.t. a positive Radon measure supported on a closed subset $K$ of the character space…
The value of spectral form factor at the origin, called level compressibility, is an important characteristic of random spectra. The paper is devoted to analytical calculations of this quantity for different random unitary matrices…
In this paper, we introduce and study a unitary matrix-valued process which is closely related to the Hermitian matrix-Jacobi process. It is precisely defined as the product of a deterministic self-adjoint symmetry and a randomly-rotated…
We investigate the implications of free probability for random matrices. From rules for calculating all possible joint moments of two free random matrices, we develop a notion of partial freeness which is quantified by the breakdown of…
We combine concepts from random matrix theory and free probability together with ideas from the theory of commutator length in groups and maps from surfaces, and establish new connections between the two. More particularly, we study…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
This paper is devoted to the distribution of the eigenvalues of $XUYU^t$ where $X$ and $Y$ are given symmetric matrices and $U$ is a random real valued square matrix of standard normal distribution. More specifically we look at its moments,…
We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few body operators in chaotic many-body…
Empirical researchers often trim observations with small denominator A when they estimate moments of the form E[B/A]. Large trimming is a common practice to mitigate variance, but it incurs large trimming bias. This paper provides a novel…
Since the seminal work of Keating and Snaith, the characteristic polynomial of a random Haar-distributed unitary matrix has seen several of its functional studied or turned into a conjecture; for instance: $ \bullet $ its value in $1$…