Related papers: Measuring maximal eigenvalue distribution of Wisha…
We present a technique for simultaneous power-combining and wavelength-conversion of multiple fiber lasers into a single, lower wavelength in a different band through Raman-based, nonlinear power combining. We illustrate this by power…
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…
The distribution of the apparent total energy emitted by a gamma-ray burst reflects not only the distribution of the energy actually released by the burst engine, but also the distribution of beaming angles. Using the observed energy…
In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of…
In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…
Design of a mid-wave IR (MWIR) broad-band fiber-based light source exploiting four-wave mixing (FWM) in a meter long suitably designed highly nonlinear (NL) chalcogenide microstructured optical fiber (MOF) is reported. This superior FWM…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
By tailoring probabilistic constellation shaping (PCS) for nonlinearity tolerance, we experimentally demonstrate up to 1.1 dB increase in signal-to-noise ratio (SNR) and 6.4% increase in total net data rate (NDR) compared to…
We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index beta=1,2 and 4. Our generalised model has a fat-tailed distribution while preserving the invariance…
This paper proposes a unified approach that enables the Wishart distribution to be studied simultaneously in the real, complex, quaternion and octonion cases. In particular, the noncentral generalised Wishart distribution, the joint density…
Let $X$ be an $M\times N$ random matrix consisting of independent $M$-variate elliptically distributed column vectors $\mathbf{x}_{1},\dots,\mathbf{x}_{N}$ with general population covariance matrix $\Sigma$. In the literature, the quantity…
We consider rectangular random matrices of size $p\times n$ belonging to the real Wishart-Laguerre ensemble also known as the chiral Gaussian orthogonal ensemble. This ensemble appears in many applications like QCD, mesoscopic physics, and…
Optical quantum technologies such as quantum sensing, quantum cryptography and quantum computation all utilize properties of non-classical light, such as precise photon-number and entangled photon-pair states, to surpass technologies based…
An ultrafast laser delivering 10.4 kW average output power based on coherent combination of twelve stepindex fiber amplifiers is presented. The system emits close-to-transform-limited 254 fs pulses at 80 MHz repetition rate, has a high beam…
We solve the largest sample eigenvalue distribution problem in the rank 1 spiked model of the quaternionic Wishart ensemble, which is the first case of a statistical generalization of the Laguerre symplectic ensemble (LSE) on the soft edge.…
We consider $N\times N$ random matrices of the form $H = W + V$ where $W$ is a real symmetric Wigner matrix and $V$ a random or deterministic, real, diagonal matrix whose entries are independent of $W$. We assume subexponential decay for…
We revisit the matching conditions for self-guided laser pulse propagation in plasma and refine their formulation to maximize the energy of electrons produced via laser wakefield acceleration. Bayesian optimization, combined with…
Recently, it was shown that the probability distribution function (PDF) of the free energy of a single continuum directed polymer (DP) in a random potential, equivalently of the height of a growing interface described by the…
We describe a tunable broadband mid-infrared laser source based on difference-frequency mixing of a 100 MHz femtosecond Yb:fiber laser oscillator and a Raman-shifted soliton generated with the same laser. The resulting light is tunable over…
We consider sample covariance matrices of the form $\mathcal{Q}=(\Sigma^{1/2}X)(\Sigma^{1/2} X)^*$, where the sample $X$ is an $M\times N$ random matrix whose entries are real independent random variables with variance $1/N$ and where…