Marginal stability constrains force and pair distributions at random close packing.

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The jamming transition as a paradigm to understand the loss landscape of deep neural networks (2018, background): “In glassy systems, such power-laws reveal properties that cannot be reached by studying the Hessian, in particular the fact that the dynamics occurs via broadly distributed avalanches [42–44], indicative of a hierarchical organization of the landscape [45].”
Edwards Statistical Mechanics for Jammed Granular Matter (2016, background): “The existence of this power-law has been explained by the marginal stability of the packing which is controlled by small forces (Wyart, 2012).”
Fractal free energy landscapes in structural glasses (2014, background): “These scalings of g(r) are crucial for determining the mechanical stability of packings [40, 51].”