Related papers: Measuring maximal eigenvalue distribution of Wisha…
Vinberg cones and the ambient vector spaces are important in modern statistics of sparse models and of graphical models. The aim of this paper is to study eigenvalue distributions of Gaussian, Wigner and covariance matrices related to…
We propose the exact calculation of the probability density function (PDF) and cumulative distribution function (CDF) of mutual information (MI) for a two-user MIMO MAC network over block Rayleigh fading channels. So far the PDF and CDF…
Light source is indispensable component in on-chip system. Compared with hybrid or heterogeneous integrated laser, monolithically integrated laser is more suitable for high density photonic integrated circuit (PIC) since the capability of…
We report the analysis of simultaneous multi-wavelength data of the high energy peaked blazar RGB J0710+591 from the LAXPC, SXT and UVIT instruments on-board AstroSat. The wide band X-ray spectrum (0.35 -- 30 keV) is modelled as synchrotron…
Probabilistic shaping for intensity modulation and direct detection (IM/DD) links is discussed and a peak power constraint determined by the limited modulation extinction ratio (ER) of optical modulators is introduced. The input…
We investigate whether the Wigner semi-circle and Marcenko-Pastur distributions, often used for deep neural network theoretical analysis, match empirically observed spectral densities. We find that even allowing for outliers, the observed…
We consider $N\times N$ Hermitian or symmetric random matrices with independent entries. The distribution of the $(i,j)$-th matrix element is given by a probability measure $\nu_{ij}$ whose first two moments coincide with those of the…
We report on the depletion and power amplification of the driving laser pulse in a strongly-driven laser wakefield accelerator. Simultaneous measurement of the transmitted pulse energy and temporal shape indicate an increase in peak power…
Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…
Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology and economy. In this work we develop a theory for the eigenvalue fluctuations of diluted…
Let $A$ be a real skew-symmetric Gaussian random matrix whose upper triangular elements are independently distributed according to the standard normal distribution. We provide the distribution of the largest singular value $\sigma_1$ of…
This paper focuses on the non-asymptotic concentration of the heteroskedastic Wishart-type matrices. Suppose $Z$ is a $p_1$-by-$p_2$ random matrix and $Z_{ij} \sim N(0,\sigma_{ij}^2)$ independently, we prove the expected spectral norm of…
Efficient schemes for sampling from the eigenvalues of the Wishart distribution have recently been described for both the uncorrelated central case (where the covariance matrix is $\mathbf{I}$) and the spiked Wishart with a single spike…
Flexible and tensile wavelength-tunable micrometer-sized random lasers in the form of microporous polymer fiber are demonstrated. The fibers are fabricated by directly drawing from an aqueous mixture and subsequently selective chemical…
Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic distributions near the phase transition in…
We demonstrate a new high efficiency architecture for cascaded Raman fiber lasers based on a single pass cascaded amplifier configuration. Conversion is seeded at all intermediate Stokes wavelengths using a multi-wavelength seed source. A…
The properties of eigenvalues of large dimensional random matrices have received considerable attention. One important achievement is the existence and identification of the limiting spectral distribution of the empirical spectral…
Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated…
We propose a robust spectral beam combining scheme using wavelength dependent polarisation rotators and polarization beam combiners. We successfully demonstrated the concept for two Yb-doped fiber lasers at 1064nm and 1092nm up to a total…
In the past decade, complex networks of light emitters are proposed as novel platforms for photonic circuits and lab-on-chip active devices. Lasing networks made by connected multiple gain components and graphs of nanoscale random lasers…