Edgeworth expansions for the product of two complex random matrices each with IID components

Christopher S. Withers (1) , Saralees Nadarajah (2)

1 Applied Mathematics Group Industrial Research Limited Lower Hutt
2 Respiratory Research Group

Let and be independent complex matrices with elements i.i.d. as and , respectively, where , and are independent and identically distributed, and are independent and identically distributed. We obtain Edgeworth expansions for the distribution of any element of (and so for trace ), in Cartesian coordinates. If or is symmetric about zero, the expansions are given to . A specific example applicable to reverberation systems is the case when and are both Gaussian.

Mots clés: Complex random matrices; Edgeworth expansions; Gaussian

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Christopher S. Withers, Saralees Nadarajah. Edgeworth expansions for the product of two complex random matrices each with IID components. Statistics and Probability Letters, 2010, 80 (23-24), pp.1954. ⟨10.1016/j.spl.2010.08.025⟩. ⟨hal-00691778⟩