Circular averages and Falconer/Erdös distance conjecture in the plane for random metrics

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An improved result for Falconer’s distance set problem in even dimensions (2020, background): “For the best previously known bounds in higher dimensions for general metrics, see, for example, [12] and [13].”
Multilinear generalized Radon transforms and point configurations (2012, methodology): “The purpose of this section is to use a variant of a “continuous-to-discrete” mechanism, developed in [19, 21, 20, 23], to show that Thms.”
Average decay of the Fourier transform of measures with applications (2015, background): “Indeed, there is an extensive literature regarding averages over different manifolds and other generalisations; see for example [10, 11, 22, 23, 35] and the references therein.”