Quadratic Forms in Random Matrices with Applications in Spectrum Sensing by Daniel Gaetano Riviello, Giusi Alfano, Roberto Garello

“…In particular, recent advancements in spectral characterization of finite-dimensional random matrices from the so-called <i>polynomial ensembles</i> allow for the analysis of several scenarios of interest in wireless communications and signal processing. …”
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The Exact Distribution of the Condition Number of Complex Random Matrices by Lin Shi, Taibin Gan, Hong Zhu, Xianming Gu

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Second-Order Moment Convergence Rates for Spectral Statistics of Random Matrices by Junshan Xie

“…This paper considers the precise asymptotics of the spectral statistics of random matrices. Following the ideas of Gut and Spătaru (2000) and Liu and Lin (2006) on the precise asymptotics of i.i.d. random variables in the context of the complete convergence and the second-order moment convergence, respectively, we will establish the precise second-order moment convergence rates of a type of series constructed by the spectral statistics of Wigner matrices or sample covariance matrices.…”
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Tail Bounds for ℓ1 Norm of Gaussian Random Matrices with Applications by Xianjie Gao, Mingliang Zhang, Jinming Luo

“…Tail bounds for eigenvalues of Gaussian random matrices are one of the hot study problems. In this paper, we present tail and expectation bounds for the ℓ1 norm of Gaussian random matrices, respectively. …”
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Impact of a block structure on the Lotka-Volterra model by Clenet, Maxime, Massol, François, Najim, Jamal

Subjects: “…Lotka-Volterra model, Block structure, Linear Complementarity Problems, Large Random Matrices, Stability of food webs.…”
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Compressed Sensing Based Apple Image Measurement Matrix Selection by Ying Xiao, Wanlin Gao, Ganghong Zhang, Han Zhang

“…This paper firstly chooses sym5 wavelet base as apple image sparse transformation base, and then it uses Gaussian random matrices, Bernoulli random matrices, Partial Orthogonal random matrices, Partial Hadamard matrices, and Toeplitz matrices to measure apple images, respectively. …”
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Integrated photonic programmable random matrix generator with minimal active components by Kevin Zelaya, Mostafa Honari-Latifpour, Mohammad-Ali Miri

“…Abstract Random matrices are fundamental in photonic computing because of their ability to model and enhance complex light interactions and signal processing capabilities. …”
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Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking by Gernot Akemann, Federico Balducci, Aurélia Chenu, Patricia Päßler, Federico Roccati, Ruth Shir

“…We confirm that such an effective description of random matrices also applies in classes AI^{†} and AII^{†} up to next-to-nearest-neighbor spacings.…”
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On the function TreH+itK by Mark Fannes, Dénes Petz

“…This shows that the Bessis-Moussa-Vilani conjecture holds for large random matrices in an asymptotic sense.…”
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Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach by Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov

“…By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $\rho(E)$ for the Lévy and the Lévy -Rosenzweig-Porter random matrices which off-diagonal elements are strongly non-Gaussian with power-law tails. …”
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Properties of Matrix Variate Confluent Hypergeometric Function Distribution by Arjun K. Gupta, Daya K. Nagar, Luz Estela Sánchez

“…We also derive density functions of X2-1/2X1X2-1/2, (X1+X2)-1/2X1(X1+X2)-1/2, and X1+X2, where m×m independent random matrices X1 and X2 follow confluent hypergeometric function kind 1 and gamma distributions, respectively.…”
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Fast reconstruction method for compressed sensing model with semi-tensor product by Jinming WANG, Shiping YE, Lizhe YU, Sen XU, Yanjun JIANG

“…To reduce the storage space of random measurement matrix and improve the reconstruction efficiency for compressed sensing (CS),a new sampling approach for CS with semi-tensor product (STP-CS) was proposed.The proposed approach generated a low dimensional random measurement matrix to sample the sparse signals.Then the solutions of the sparse vector were estimated group by group with a l_q-minimization (0＆lt;q＆lt;1) iteratively re-weighted least-squares (IRLS) algorithm.Compared with traditional compressed sensing methods,the proposed approach outperformed conventional CS in speed of reconstruction and that it also obtained comparable quality in the reconstruction.Numerical experiments were conducted using gray-scale images,the peak signal-to-noise ratio (PSNR) and the reconstruction time of the reconstruction images were compared with the random matrices with different dimensions.Comparisons were also conducted with other low storage techniques.Numerical experiment results show that the STP-CS can effectively reduce the storage space of the random measurement matrix to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <mfrac> <mi>M</mi> <mi>t</mi> </mfrac> <mtext>×</mtext><mfrac> <mi>N</mi> <mi>t</mi> </mfrac> </math></inline-formula> and decrease tow orders of magnitude of time that for conventional CS,while maintaining the reconstruction quality.Numerical results also show that the reconstruction time can be effectively improved 260 for the image size of 1 024×1 024.…”
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Analysis of Stationary Random Responses for Non-Parametric Probabilistic Systems by Y. Zhao, Y.H. Zhang, J.H. Lin, W.P. Howson, F.W. Williams

“…In this paper, the random uncertainties of the mass, damping and stiffness matrices in a finite element model are replaced by random matrices, and a highly efficient pseudo excitation method for the dynamic response analysis of non-parametric probability systems subjected to stationary random loads is developed. …”
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Portfolio Optimization and Random Matrix Theory in Stock Exchange by mostafa heidari haratemeh

“…In other words, the risk is reduced by identifying and removing non-valuable stocks from the portfolio portfolio. c) A stochastic stock matrix can significantly predict the realized return and risk of the market and, therefore, explain the risk of market information. d) The inverse participation ratio determines the stocks affecting the particular vectors, and the primary analysis of random matrices is based on adjusting this ratio using random matrix clearance.Originality/Value: Unlike other portfolio formation methods determining the weight of each asset in the portfolio, stochastic matrix theory identifies unused stocks and removes them from the stock portfolio, thereby improving portfolio return and risk.…”
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Cantelli’s Bounds for Generalized Tail Inequalities by Nicola Apollonio

“…Three diverse applications to random matrices, tails of linear images of random vectors, and network homophily are also given.…”
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