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Studying the jamming transition of granular and colloidal systems, has leadto a proliferation of theoretical and numerical results formulated in thelanguage of the eigenspectrum of the dynamical matrix for these disorderedsystem. Only recently however, these modes have been accessed experimentally incolloidal and granular media, computing the eigenmodes of the covariance matrixof the particle positions. At the same time new conceptual and methodologicalquestions have appeared, regarding the interpretation of these results. In thepresent paper, we first give an overview of the theoretical framework which isappropriate to discuss the interpretation of the eigenmodes and eigenvalues ofthe correlation matrix in terms of the vibrational properties of these systems.  We then illustrate several aspects of the statistical and data analysistechniques which are necessary to extract reliable results from experimentaldata. Concentrating on the case of hard sphere simulations, colloidal andgranular experiments, we discuss how to test the existence of a metastablestate, the statistical independence of the sampling, the effect of theexperimental resolution, and the harmonic hypothesis underlying the approach,highlighting both its promises and limitations.

Dynamical fluctuations close to Jamming versus Vibrational Modes : a  pedagogical discussion illustrated on hard spheres simulations, colloidal and  granular experiments