相关论文: The moduli space of twisted Laplacians and random …

We consider random n-covers $X_n$ of an arbitrary compact hyperbolic surface $X$. We show that in the large n regime and small window limit, the variance of the smooth spectral statistics of the Laplacian twisted by a unitary abelian…

Let $(X,g)$ be a closed, connected surface, with variable negative curvature. We consider the distribution of eigenvalues of the Laplacian on random covers $X_n\to X$ of degree $n$. We focus on the ensemble variance of the smoothed number…

We show that there is a constant $c>0$ such that a genus $g$ closed hyperbolic surface, sampled at random from the moduli space $\mathcal{M}_{g}$ with respect to the Weil-Petersson probability measure, has Laplacian spectral gap at least…

We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…

The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles…

We study smooth linear spectral statistics of twisted Laplacians on random $n$-covers of a fixed compact hyperbolic surface $X$. We consider two aspects of such statistics. The first is the fluctuations of such statistics in a small energy…

We study the geometry and spectral theory of Weil-Petersson random surfaces with genus-$g$ and $n$ cusps in the large-$n$ limit. We show that for a random hyperbolic surface in $\mathcal{M}_{g,n}$ with $n$ large, the number of small…

Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…

We consider powers of the absolute value of the characteristic polynomial of Haar distributed random orthogonal or symplectic matrices, as well as powers of the exponential of its argument, as a random measure on the unit circle minus small…

Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…

We study the fluctuations of smooth linear statistics of Laplace eigenvalues of compact hyperbolic surfaces lying in short energy windows, when averaged over the moduli space of surfaces of a given genus. The average is taken with respect…

We introduce random matrix ensembles that correspond to the infinite families of irreducible Riemannian symmetric spaces of type I. In particular, we recover the Circular Orthogonal and Symplectic Ensembles of Dyson, and find other families…

We study the variance of a linear statistic of the Laplace eigenvalues on a hyperbolic surface, when the surface varies over the moduli space of all surfaces of fixed genus, sampled at random according to the Weil-Petersson measure. The…

We investigate the spectral properties of all-to-all interacting spin Hamiltonians acting on exactly $k$ spins, whose coupling coefficients are drawn from a normal distribution with mean $\mu$ and variance $\sigma^2$. For $\mu = 0$, we…

In this paper, we show how to use the framework of mod-Gaussian convergence in order to study the fluctuations of certain models of random graphs, of random permutations and of random integer partitions. We prove that, in these three…

We study the spectral geometric properties of the scalar Laplace-Beltrami operator associated to the Weil-Petersson metric $g_{\mathrm{WP}}$ on $\mathcal M_\gamma$, the Riemann moduli space of surfaces of genus $\gamma > 1$. This space has…

The ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra. It does not require the knowledge of density of states and is therefore quite convenient to…

Spectral statistics of quantum chaotic systems are governed by random matrix universality. In many cases of interest, time-reversal symmetry selects the Gaussian Orthogonal Ensemble (GOE) as the relevant universality class. In holographic…

We consider random stochastic matrices $M$ with elements given by $M_{ij}=|U_{ij}|^2$, with $U$ being uniformly distributed on one of the classical compact Lie groups or associated symmetric spaces. We observe numerically that, for large…

In this article, we study the Dirac spectrum of typical hyperbolic surfaces of finite area, equipped with a nontrivial spin structure (so that the Dirac spectrum is discrete). For random Weil-Petersson surfaces of large genus $g$ with…