5,669 research outputs found
Financial Applications of Random Matrix Theory: a short review
We discuss the applications of Random Matrix Theory in the context of
financial markets and econometric models, a topic about which a considerable
number of papers have been devoted to in the last decade. This mini-review is
intended to guide the reader through various theoretical results (the
Marcenko-Pastur spectrum and its various generalisations, random SVD, free
matrices, largest eigenvalue statistics, etc.) as well as some concrete
applications to portfolio optimisation and out-of-sample risk estimation.Comment: To appear in the "Handbook on Random Matrix Theory", Oxford
University Pres
Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles
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
P\'ech\'e, 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 -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.Comment: 39 pages, 4 figures; v2: 43 pages, presentation of Thm 1.4 improved,
alternative proof of Prop 3.1 and reference added; v3: final typo
corrections, to appear in AIHP Probabilite et Statistiqu
Output Statistics of MIMO Channels with General Input Distribution
The information that can be conveyed through a wireless channel, with multiple-antenna equipped transmitter and receiver, crucially depends on the channel behavior as well as on the input structure. In this paper, we derive analytical results, concerning the probability density function (pdf) of the output of a single-user, multiple-antenna communication. The analysis is carried out under the assumption of an optimized input structure, and assuming Gaussian noise and a Rayleigh block-fading channel. Our analysis therefore provides a quite general and compact expression for the conditional output pdf. We also highlight the relation between such an expression and the results already available in the literature for some specific input structure
- …