2019/07/17 by Jérémie Bigot, Bigot, Jérémie, Camille Male +1 · 2 citations
Mathematics · #62G05 #62H12 #Advanced Combinatorial Mathematics #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1907.07753
openalex publication_date 2019/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the eigenvalue distribution of a GUE matrix with a variance profile\nthat is perturbed by an additive random matrix that may possess spikes. Our\napproach is guided by Voiculescu's notion of freeness with amalgamation over\nthe diagonal and by the notion of deterministic equivalent. This allows to\nderive a fixed point equation to approximate the spectral distribution of\ncertain deformed GUE matrices with a variance profile and to characterize the\nlocation of potential outliers in such models in a non-asymptotic setting. We\nalso consider the singular values distribution of a rectangular Gaussian random\nmatrix with a variance profile in a similar setting of additive perturbation.\nWe discuss the application of this approach to the study of low-rank matrix\ndenoising models in the presence of heteroscedastic noise, that is when the\namount of variance in the observed data matrix may change from entry to entry.\nNumerical experiments are used to illustrate our results.\n