@article{8373,
abstract = {It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim.},
author = {Pitrik, József and Virosztek, Daniel},
issn = {0024-3795},
journal = {Linear Algebra and its Applications},
keywords = {Kubo-Ando mean, weighted multivariate mean, barycenter},
pages = {203--217},
publisher = {Elsevier},
title = {{A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means}},
doi = {10.1016/j.laa.2020.09.007},
volume = {609},
year = {2020},
}
@article{72,
abstract = {We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle initially at the origin. For ρ<λ, there is a shock and the second class particle moves with speed 1−λ−ρ. For large time t, we show that the position of the second class particle fluctuates on a t1/3 scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time t.},
author = {Ferrari, Patrick and Ghosal, Promit and Nejjar, Peter},
issn = {02460203},
journal = {Annales de l'institut Henri Poincare (B) Probability and Statistics},
number = {3},
pages = {1203--1225},
publisher = {IHP},
title = {{Limit law of a second class particle in TASEP with non-random initial condition}},
doi = {10.1214/18-AIHP916},
volume = {55},
year = {2019},
}
@article{7423,
abstract = {We compare finite rank perturbations of the following three ensembles of complex rectangular random matrices: First, a generalised Wishart ensemble with one random and two fixed correlation matrices introduced by Borodin and Péché, second, the product of two independent random matrices where one has correlated entries, and third, the case when the two random matrices become also coupled through a fixed matrix. The singular value statistics of all three ensembles is shown to be determinantal and we derive double contour integral representations for their respective kernels. Three different kernels are found in the limit of infinite matrix dimension at the origin of the spectrum. They depend on finite rank perturbations of the correlation and coupling matrices and are shown to be integrable. The first kernel (I) is found for two independent matrices from the second, and two weakly coupled matrices from the third ensemble. It generalises the Meijer G-kernel for two independent and uncorrelated matrices. The third kernel (III) is obtained for the generalised Wishart ensemble and for two strongly coupled matrices. It further generalises the perturbed Bessel kernel of Desrosiers and Forrester. Finally, kernel (II), found for the ensemble of two coupled matrices, provides an interpolation between the kernels (I) and (III), generalising previous findings of part of the authors.},
author = {Akemann, Gernot and Checinski, Tomasz and Liu, Dangzheng and Strahov, Eugene},
issn = {0246-0203},
journal = {Annales de l'Institut Henri Poincaré, Probabilités et Statistiques},
number = {1},
pages = {441--479},
publisher = {Institute of Mathematical Statistics},
title = {{Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles}},
doi = {10.1214/18-aihp888},
volume = {55},
year = {2019},
}
@article{405,
abstract = {We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which has been introduced by Chen and Tropp quite recently.},
author = {Virosztek, Daniel},
journal = {Linear Algebra and Its Applications},
pages = {67--78},
publisher = {Elsevier},
title = {{Jointly convex quantum Jensen divergences}},
doi = {10.1016/j.laa.2018.03.002},
volume = {576},
year = {2019},
}
@article{429,
abstract = {We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.},
author = {Ajanki, Oskari H and Erdös, László and Krüger, Torben H},
issn = {14322064},
journal = {Probability Theory and Related Fields},
number = {1-2},
pages = {293–373},
publisher = {Springer},
title = {{Stability of the matrix Dyson equation and random matrices with correlations}},
doi = {10.1007/s00440-018-0835-z},
volume = {173},
year = {2019},
}