Probability theory and related fields, 2009-07, Vol.144 (3-4), p.471-515
2009
Details
- Autor(en) / Beteiligte
- Titel
- Rectangular random matrices, related convolution
- Ist Teil von
- Probability theory and related fields, 2009-07, Vol.144 (3-4), p.471-515
- Ort / Verlag
- Berlin/Heidelberg: Springer-Verlag
- Erscheinungsjahr
- 2009
- Link zum Volltext
- Quelle
- EBSCOhost Business Source Ultimate
- Beschreibungen/Notizen
- We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates. It appears that one can compute the limits of all noncommutative moments (thus all spectral properties) of the random matrices we consider because, when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically free with amalgamation over a subalgebra. Therefore, we can define a “rectangular-free convolution”, which allows to deduce the singular values of the sum of two large independent rectangular random matrices from the individual singular values. This convolution is linearized by cumulants and by an analytic integral transform, that we called the “rectangular R -transform”.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0178-8051eISSN: 1432-2064DOI: 10.1007/s00440-008-0152-zTitel-ID: cdi_hal_primary_oai_HAL_hal_00400346v1
- Format
- –
- Schlagworte
- Asymptotic properties, Convolution, Distribution theory, Economics, Eigenvalues, Exact sciences and technology, Finance, General topics, Insurance, Integral transforms, Management, Mathematical and Computational Biology, Mathematical and Computational Physics, Mathematical models, Mathematics, Mathematics and Statistics, Operations Research/Decision Theory, Probability, Probability and statistics, Probability Theory and Stochastic Processes, Quantitative Finance, Sciences and techniques of general use, Statistics, Statistics for Business, Studies, Theoretical, Theory