Extension to General Centered Atomic Spike Priors

Establish that the identical-search algorithm for the doubly sparse spiked Wigner model can be implemented for any centered atomic spike prior, rather than only for the sparse Rademacher prior.

Background

The paper analyzes a doubly sparse spiked Wigner model in which the spike has an independently sampled sparse support and the nonzero entries follow a specified prior. Its identical-search method exploits the atomic nature of a Rademacher spike: noise-free entries in the planted support take exactly the values 7b8/(np), allowing the algorithm to identify support vertices and recover relative signs by graph traversal.

The authors prove distinguishability and exact recovery for the sparse Rademacher prior, but indicate that the same construction should extend to a broader class of centered atomic priors. Establishing this extension would clarify how much of the identical-search phenomenon depends specifically on the two-point Rademacher distribution.