Results 11 to 20 of about 5,585,535 (119)
Studies on the Marchenko–Pastur Law
MathematicsIn free probability, the theory of Cauchy–Stieltjes Kernel (CSK) families has recently been introduced. This theory is about a set of probability measures defined using the Cauchy kernel similarly to natural exponential families in classical probability ...
Ayed. R. A. Alanzi +3 more
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On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions [PDF]
, 2008 International audienceIn this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the ...
Benaych-Georges, F. +2 more
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Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices
, 2021 Götze F, Timushev DA, Tikhomirov AN. Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices. Doklady Mathematics. 2021;104(3):332-335.We consider sparse sample covariance matrices with sparsity probability with p(n) >= c(0) log((aleph) over ...
Timushev, D. A. +2 more
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Freezing limits for Calogero–Moser–Sutherland particle models
Studies in Applied Mathematics, Volume 151, Issue 4, Page 1230-1281, November 2023., 2023 Abstract One‐dimensional interacting particle models of Calogero–Moser–Sutherland type with N particles can be regarded as diffusion processes on suitable subsets of RN$\mathbb {R}^N$ like Weyl chambers and alcoves with second‐order differential operators as generators of the transition semigroups, where these operators are singular on the boundaries ...
Michael Voit
wiley +1 more source
Detail-Preserving Image Denoising via Adaptive Clustering and Progressive PCA Thresholding
IEEE Access, 2018 This paper proposes a detail-preserving image denoising method via cluster-wise progressive principal component analysis (PCA) thresholding based on the Marchenko-Pastur (MP) law in random matrix theory.
Wenzhao Zhao +3 more
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Magnetic Resonance in Medicine, Volume 88, Issue 1, Page 365-379, July 2022., 2022 Purpose Relationships between diffusion‐weighted MRI signals and hepatocyte microstructure were investigated to inform liver diffusion MRI modeling, focusing on the following question: Can cell size and diffusivity be estimated at fixed diffusion time, realistic SNR, and negligible contribution from extracellular/extravascular water and exchange ...
Francesco Grussu +7 more
wiley +1 more source
Local Marchenko-Pastur law at the hard edge of the sample covariance ensemble [PDF]
, 2023 Consider an N by N matrix X of complex entries with iid real and imaginary parts. We show that the local density of eigenvalues of X*X converges to the Marchenko-Pastur law on the optimal scale with probability 1.
Kafetzopoulos, A, Maltsev, A
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Marchenko-Pastur law with relaxed independence conditions [PDF]
, 2019 We prove the Marchenko-Pastur law for the eigenvalues of $p \times p$ sample covariance matrices in two new situations where the data does not have independent coordinates.
Bryson, Jennifer +2 more
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Relaxing Independence in the Marchenko-Pastur Law for Random Matrices and the Application to Approximate Embeddings [PDF]
, 2019 This dissertation adds to the collection of works studying the Marchenko-Pastur law in two ways. First it considers two new models of random column vectors that have weaker independence hypotheses than the well-known i.i.d.
Bryson, Jennifer Anne
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Rate of convergence in probability to the Marchenko-Pastur law
, 2004 Götze F, Tikhomirov A. Rate of convergence in probability to the Marchenko-Pastur law. BERNOULLI. 2004;10(3):503-548.It is shown that the Kolmogorov distance between the spectral distribution function of a random covariance (1/p)XXT, where X is an nxp ...
Tikhomirov, A, Götze, Friedrich
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