Macierze losowe, ciągłe układy cyrkularne i operator trójkątny

I will discuss a realization of the limit joint *-distributions of complex independent Gaussian random matrices in terms of suitably defined creation and annihilation operators living in some direct integral of Hilbert spaces. These operators are decomposed in terms of continuous circular systems of operators acting between the fibers of the considered Hilbert space. This approach leads to a bijective proof of the formula for *-moments of the triangular operator of Dykema and Haagerup, using the enumeration formula of Chauve, Dulucq and Rechnizter for alternating ordered rooted trees.