We give the bicomplex Gaussian Fibonacci and Lucas numbers establish generating functions Binet’s formulas related to these numbers. Also, we present summation formula, matrix representation Honsberger identity their relationship between Finally, show relationships among Fibonacci, Lucas,

In this note, we study the Gaussian fluctuations for Wishart matrices d−1Xn,dXn,dT, where Xn,d is a n×d random matrix whose entries are jointly and correlated with row column covariance functions given by r s respectively such that r(0)=s(0)=1. Under assumptions s∈ℓ4/3(Z) ‖r‖ℓ1(Z)<6/2, establish n3/d convergence rate Wasserstein distance between normalization of d−1Xn,dXn,dT corresponding ensem...

In continuous-variable quantum information processing, error correction of Gaussian errors requires simultaneous estimation both quadrature components displacements on phase space. However, operators $x$ and $p$ are non-commutative conjugate observables, whose measurement is prohibited by the uncertainty principle. Gottesman-Kitaev-Preskill (GKP) deals with this problem using complex non-Gaussi...

The paper aims at presenting a didactic and self-contained overview of Gauss-Hermite and Gauss-Laguerre laser beam modes. The usual textbook approach for deriving these modes is to solve the Helmoltz electromagnetic wave equation within the paraxial approximation. Here, a different technique is presented: Using the plane wave representation of the fundamental Gaussian mode as seed function, all...