Dependently rigid characterization of the maximum likelihood threshold

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Let G=(V,E)G=(V,E)) be a graph. A framework (G,P)(G,P) in Rn\mathbb{R}^n is nn-dependently rigid if every edge-equivalent framework (G,Q)(G,Q) in Rm\mathbb{R}^m has an affinely dependent set of points, and GG is generically nn-dependently rigid if every generic framework (G,P)(G,P) in Rn\mathbb{R}^n is nn-dependently rigid.

Dependently rigidity conjecture. The maximum likelihood threshold of GG is greater than nn if and only if GG is generically nn-dependently rigid.

This conjecture is presented as a proposed connection between maximum likelihood thresholds and a stronger form of combinatorial rigidity. The supplied text does not state whether it has been resolved.

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Primary source

Elizabeth Gross and Seth Sullivant, “The Maximum Likelihood Threshold of a Graph”, arXiv:1404.6989 (2015).

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