Ranking equations cumulative

A cumulant of rank s is a symmetric tensor with (s2 + 3s + 2)/2 unique elements for a three-dimensional distribution. Like the moments p and the quasimoments c, the cumulants are descriptors of the distribution. For a onedimensional distribution, the relations between the cumulants and the moments are defined by equating the two expansions ... [Pg.33]

In the next step, we analyze the structure of the various terms generated after the application of the WT to the matrix element in our working equations and establish that we can systematically eliminate the disconnected portion of M, if we keep track of which components of the composites containing F and G are connected. This particular analysis requires the concept of cumulant decomposition [75, 80, 88, 89] of the density matrix elements of Fjt for various ranks k. Since the final working equations are connected after the elimination of the disconnected terms, the cluster amplitudes of F are connected and are compatible with the connectivity of G. ... [Pg.35]

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