On the Law of Addition of Random Matrices

被引：0
作者：
L. Pastur
V. Vasilchuk
机构：
[1] Centre de Physique Théorique de CNRS,
[2] Luminy–case 907,undefined
[3] 13288 Marseille,undefined
[4] France.¶E-mail: pastur@cpt.univ-mrs.fr,undefined
[5] U.F.R. de Mathématiques,undefined
[6] Université Paris 7,undefined
[7] 2,undefined
[8] place Jussieu,undefined
[9] 75251 Paris Cedex 05,undefined
[10] France,undefined
[11] Mathematical Division,undefined
[12] Institute for Low Temperature Physics,undefined
[13] 47,undefined
[14] Lenin Ave.,undefined
[15] 310164,undefined
[16] Kharkov,undefined
[17] Ukraine. E-mail: vasilchuk@ilt.kharkov.ua,undefined
来源：
Communications in Mathematical Physics | 2000年 / 214卷
关键词：
Functional Equation; Random Matrix; Counting Measure; Large Matrix; Matrix Order;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices An and Bn rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix Un (i.e. An+Un*BnUn) is studied in the limit of large matrix order n. Convergence in probability to a limiting nonrandom measure is established. A functional equation for the Stieltjes transform of the limiting measure in terms of limiting eigenvalue measures of An and Bn is obtained and studied.
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页码：249 / 286
页数：37
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