scholarly journals Critical Points of Random Polynomials and Characteristic Polynomials of Random Matrices

2015 ◽  
Vol 2016 (18) ◽  
pp. 5616-5651
Author(s):  
Sean O'Rourke
Keyword(s):  
Random Matrices ◽  
Critical Points ◽  
Characteristic Polynomials ◽  
Random Polynomials

scholarly journals Characteristic Polynomials of Random Matrices

2000 ◽  
Vol 214 (1) ◽  
pp. 111-135 ◽  
Author(s):  
Edouard Brézin ◽  
Shinobu Hikami
Keyword(s):  
Random Matrices ◽  
Characteristic Polynomials

scholarly journals PLANCHEREL–ROTACH FORMULAE FOR AVERAGE CHARACTERISTIC POLYNOMIALS OF PRODUCTS OF GINIBRE RANDOM MATRICES AND THE FUSS–CATALAN DISTRIBUTION

2014 ◽  
Vol 03 (01) ◽  
pp. 1450003 ◽  
Author(s):  
THORSTEN NEUSCHEL
Keyword(s):  
Random Matrices ◽  
General Class ◽  
Laguerre Polynomials ◽  
Saddle Points ◽  
Distribution Functions ◽  
Complex Method ◽  
Characteristic Polynomials ◽  
Average Characteristic ◽  
General Order ◽  
Catalan Distribution

Formulae of Plancherel–Rotach type are established for the average characteristic polynomials of Hermitian products of rectangular Ginibre random matrices on the region of zeros. These polynomials form a general class of multiple orthogonal hypergeometric polynomials generalizing the classical Laguerre polynomials. The proofs are based on a multivariate version of the complex method of saddle points. After suitable rescaling the asymptotic zero distributions for the polynomials are studied and shown to coincide with the Fuss–Catalan distributions. Moreover, introducing appropriate coordinates, elementary and explicit characterizations are derived for the densities as well as for the distribution functions of the Fuss–Catalan distributions of general order.

scholarly journals Random polynomials, random matrices andL-functions

Nonlinearity ◽  
2006 ◽  
Vol 19 (4) ◽  
pp. 919-936 ◽  
Author(s):  
David W Farmer ◽  
Francesco Mezzadri ◽  
Nina C Snaith
Keyword(s):  
Random Matrices ◽  
Random Polynomials
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