Related papers: Spectral Phase Transitions in Non-Linear Wigner Sp…
We consider $N\times N$ Gaussian random matrices, whose average density of eigenvalues has the Wigner semi-circle form over $[-\sqrt{2},\sqrt{2}]$. For such matrices, using a Coulomb gas technique, we compute the large $N$ behavior of the…
We study the crossover behavior of statistical properties of eigenvalues in a chaotic microcavity with different refractive indices. The level spacing distributions change from Wigner to Poisson distributions as the refractive index of a…
In this paper, we study the asymptotic nonnegative rank of matrices, which characterizes the asymptotic growth of the nonnegative rank of fixed nonnegative matrices under the Kronecker product. This quantity is important since it governs…
Random feature models (RFMs), two-layer networks with a randomly initialized fixed first layer and a trained linear readout, are among the simplest nonlinear predictors. Prior asymptotic analyses in the proportional high-dimensional regime…
Consider the empirical autocovariance matrix at a given non-zero time lag based on observations from a multivariate complex Gaussian stationary time series. The spectral analysis of these autocovariance matrices can be useful in certain…
Banded random matrices were introduced as a more realistic alternative to full random matrices for describing the spectral statistics of heavy nuclei. Initially considered by Wigner, they have since become a paradigmatic model for…
We study the asymptotic behavior of the Schr\"odinger equation in the presence of a nonlinearity of Hartree type in the semi-classical regime. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading…
The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov-Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the…
Linear stability analysis of speckle pattern resulting from multiple, diffuse scattering of coherent light waves in random media with intensity-dependent refractive index (noninstantaneous Kerr nonlinearity) is performed. The speckle…
In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we…
This paper addresses the asymptotic behavior of a particular type of information-plus-noise-type matrices, where the column and row number of the matrices are large and of the same order, while signals are diverged and time delays of the…
Phase transitions and the associated symmetry breaking are at the heart of many physical phenomena. Coupled systems with multiple interacting degrees of freedom provide a fertile ground for emergent dynamics that is otherwise inaccessible…
In this paper, we establish some new central limit theorems for certain spectral statistics of a high-dimensional sample covariance matrix under a divergent spectral norm population model. This model covers the divergent spiked population…
We compute analytically the dominant contribution to the tree-level bispectrum in the Starobinsky model of inflation. In this model, the potential is vacuum energy dominated but contains a subdominant linear term which changes the slope…
When some eigenvalues of a spiked multiplicative resp. additive deformation model of a Hermitian Wigner matrix resp. a sample covariance matrix separate from the bulk, we study how the corresponding eigenvectors project onto those of the…
We present long range statistical properties of a recently introduced unitary random matrix ensemble, whose short range correlations were found to describe a transition from Wigner to Poisson type as a function of a single parameter.
We prove the existence of a phase transition for a stochastic model of interacting neurons. The spiking activity of each neuron is represented by a point process having rate $1 $ whenever its membrane potential is larger than a threshold…
We study the asymptotic behavior of the spectra of matrices of the form $S_n = \frac{1}{n}XX^*$ where $X =\sum_{r=1}^K X_r$, where $X_r = A_r^\frac{1}{2}Z_rB_r^\frac{1}{2}$, $K \in \mathbb{N}$ and $A_r,B_r$ are sequences of positive…
In this work, we show the first average-case reduction transforming the sparse Spiked Covariance Model into the sparse Spiked Wigner Model and as a consequence obtain the first computational equivalence result between two well-studied…
One-rank perturbations of Wigner matrices have been closely studied: let $P=\frac{1}{\sqrt{n}}A+\theta vv^T$ with $A=(a_{ij})_{1 \leq i,j \leq n} \in \mathbb{R}^{n \times n}$ symmetric, $(a_{ij})_{1 \leq i \leq j \leq n}$ i.i.d. with…