scholarly journals Microwave Realization of the Gaussian Symplectic Ensemble

2016 ◽  
Vol 117 (6) ◽  
Author(s):  
A. Rehemanjiang ◽  
M. Allgaier ◽  
C. H. Joyner ◽  
S. Müller ◽  
M. Sieber ◽  
...  
Keyword(s):  
Gaussian Symplectic Ensemble

scholarly journals A generalization of Mehta-Wang determinant and Askey-Wilson polynomials

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Victor J. W. Guo ◽  
Masao Ishikawa ◽  
Hiroyuki Tagawa ◽  
Jiang Zeng
Keyword(s):  
Gamma Function ◽  
Jacobi Polynomials ◽  
The Other ◽  
Two Dimensional ◽  
Moment Sequence ◽  
International Audience ◽  
Pfaffian Formula ◽  
The Moment ◽  
Wilson Polynomials ◽  
Gaussian Symplectic Ensemble

International audience Motivated by the Gaussian symplectic ensemble, Mehta and Wang evaluated the $n×n$ determinant $\det ((a+j-i)Γ (b+j+i))$ in 2000. When $a=0$, Ciucu and Krattenthaler computed the associated Pfaffian $\mathrm{Pf}((j-i)Γ (b+j+i))$ with an application to the two dimensional dimer system in 2011. Recently we have generalized the latter Pfaffian formula with a $q$-analogue by replacing the Gamma function by the moment sequence of the little $q$-Jacobi polynomials. On the other hand, Nishizawa has found a q-analogue of the Mehta–Wang formula. Our purpose is to generalize both the Mehta-Wang and Nishizawa formulae by using the moment sequence of the little $q$-Jacobi polynomials. It turns out that the corresponding determinant can be evaluated explicitly in terms of the Askey-Wilson polynomials.

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