相关论文: Upper tail large deviations for extremal eigenvalu…

We study real eigenvalues of $N\times N$ real elliptic Ginibre matrices indexed by a non-Hermiticity parameter $0\leq \tau<1$, in both the strong and weak non-Hermiticity regime. Here $N$ is assumed to be an even number. In both regimes, we…

We consider the elliptic Ginibre matrices in the orthogonal symmetry class that interpolates between the real Ginibre ensemble and the Gaussian orthogonal ensemble. We obtain the finite size corrections of the real eigenvalue densities in…

Starting from one-point tail bounds, we establish an upper tail large deviation principle for the directed landscape at the metric level. Metrics of finite rate are in one-to-one correspondence with measures supported on a set of countably…

In this paper we consider the extreme behavior of the extremal eigenvalues of white Wishart matrices, which plays an important role in multivariate analysis. In particular, we focus on the case when the dimension of the feature p is much…

This paper studies the joint limiting behavior of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model, where the asymptotic regime is such that the dimension and sample size grow…

For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…

Consider a random sample from a bivariate distribution function $F$ in the max-domain of attraction of an extreme-value distribution function $G$. This $G$ is characterized by two extreme-value indices and a spectral measure, the latter…

We study the maximum of the random assignment process on rectangular matrices. We derive first-order asymptotics for the expected maximum, prove a law of large numbers under mild tail assumptions, and obtain exponential upper bounds for the…

Under scenario of high frequency data, consistent estimator of realized Laplace transform of volatility is proposed by \citet{TT2012a} and related central limit theorem has been well established. In this paper, we investigate the asymptotic…

We develop a new probabilistic and geometric method to obtain several sharp results pertaining to the upper tail behavior of continuum Gibbs measures on infinite ensembles of random continuous curves, also known as line ensembles,…

We compute the leading asymptotics of the maximum of the (centered) logarithm of the absolute value of the characteristic polynomial, denoted $\Psi_N$, of the Ginibre ensemble as the dimension $N$ of the random matrix tends to infinity. The…

We consider the random normal matrices with quadratic external potentials where the associated orthogonal polynomials are Hermite polynomials and the limiting support (called droplet) of the eigenvalues is an ellipse. We calculate the…

In this paper, we characterize the asymptotic and large scale behavior of the eigenvalues of wavelet random matrices in high dimensions. We assume that possibly non-Gaussian, finite-variance $p$-variate measurements are made of a…

The probability that the sum of independent, centered, identically distributed, heavy-tailed random variables achieves a very large value is asymptotically equal to the probability that there exists a single summand equalling that value. We…

In this paper we study an ensemble of random matrices called Elliptic Volatility Model, which arises in finance as models of stock returns. This model consists of a product of independent matrices $X = \Sigma Z $ where $Z$ is a $T$ by $S$…

We study the asymptotic behavior of outliers in the spectrum of bounded rank perturbations of large random matrices. In particular, we consider perturbations of elliptic random matrices which generalize both Wigner random matrices and…

In this article, we compute and compare the statistics of the number of eigenvalues in a centred disc of radius $R$ in all three Ginibre ensembles. We determine the mean and variance as functions of $R$ in the vicinity of the origin, where…

The class of Dirichlet random vectors is central in numerous probabilistic and statistical applications. The main result of this paper derives the exact tail asymptotics of the aggregated risk of powers of Dirichlet random vectors when the…

Complex systems, and in particular random neural networks, are often described by randomly interacting dynamical systems with no specific symmetry. In that context, characterizing the number of relevant directions necessitates fine…

Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a data set has been collected under normal…