相关论文: Polynuclear growth model, GOE$^2$ and random matri…

We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…

In this study, we derive the exact distributions of eigenvalues of a singular Wishart matrix under an elliptical model. We define generalized heterogeneous hypergeometric functions with two matrix arguments and provide convergence…

Under certain conditions, the largest eigenvalue of a sample covariance matrix undergoes a well-known phase transition when the sample size $n$ and data dimension $p$ diverge proportionally. In the subcritical regime, this eigenvalue has…

The authors consider the length, $l_N$, of the length of the longest increasing subsequence of a random permutation of $N$ numbers. The main result in this paper is a proof that the distribution function for $l_N$, suitably centered and…

The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in…

We study a class of random matrices that appear in several communication and signal processing applications, and whose asymptotic eigenvalue distribution is closely related to the reconstruction error of an irregularly sampled bandlimited…

We develop a method for the random sampling of (multimode) Gaussian states in terms of their covariance matrix, which we refer to as a random quantum covariance matrix (RQCM). We analyze the distribution of marginals and demonstrate that…

Random Hermitian matrices with a source term arise, for instance, in the study of non-intersecting Brownian walkers \cite{Adler:2009a, Daems:2007} and sample covariance matrices \cite{Baik:2005}. We consider the case when the $n\times n$…

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on…

We show that the reformulation of the geometric Robinson-Schensted-Knuth (gRSK) correspondence via local moves, introduced in \cite{OSZ14} can be extended to cases where the input matrix is replaced by more general polygonal,…

We consider a full rank deformation of the GUE $W_N+A_N$ where $A_N$ is a full rank Hermitian matrix of size $N$ and $W_N$ is a GUE. The empirical eigenvalue distribution $\mu_{A_N}$ of $A_N$ converges to a probability distribution $\nu$.…

In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution, We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of…

We propose a theoretical framework to study the eigenvalue spectra of the controllability Gramian of systems with random state matrices, such as networked systems with a random graph structure. Using random matrix theory, we provide…

Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds…

In this paper non-asymptotic exact exponential estimates are derived for the tail of maximum distribution of random field in the terms of majoring measures or, equally, generic chaining.

Let $\sqrt{N}+\lambda_{max}$ be the largest real eigenvalue of a random $N\times N$ matrix with independent $N(0,1)$ entries (the `real Ginibre matrix'). We study the large deviations behaviour of the limiting $N\rightarrow \infty$…

We show that the limiting minimal eigenvalue distributions for a natural generalization of Gaussian sample-covariance structures (the "beta ensembles") are described by the spectrum of a random diffusion generator. By a Riccati…

Generative models aim to learn the distribution of datasets, such as images, so as to be able to generate samples that statistically resemble real data. However, learning the underlying probability distribution can be very challenging and…

We study the fluctuations of the largest eigenvalue $\lambda_{\max}$ of $N \times N$ random matrices in the limit of large $N$. The main focus is on Gaussian $\beta$-ensembles, including in particular the Gaussian orthogonal ($\beta=1$),…

We study the sample covariance matrix for real-valued data with general population covariance, as well as MANOVA-type covariance estimators in variance components models under null hypotheses of global sphericity. In the limit as matrix…