Rectangular random matrices, related convolution

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Free Probability and Random Matrices (2014, background): “Extensions of the theory to rectangular matrices can be found in [11], and to “second order freeness” (describing ﬂuctuations of random matrices) in [16].”
The singular values and vectors of low rank perturbations of large rectangular random matrices (2011, background): “The critical value also depends on the aforementioned integral transforms which arise from rectangular free probability theory [11, 12].”
The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices (2009, background): “ random matrices. There too, a phase transition occurs at a threshold determined by an integral transform which plays an analogous role in the computation of the rectangular additive free convolution [7, 8, 9]. The emergence of these transforms in the context of the study of the extreme or isolated ”