POISSON HYPOTHESIS AND LARGE-POPULATION LIMIT FOR NETWORKS OF SPIKING NEURONS

The candidate’s two claims align with the paper’s two main theorems. Part A (mean-field limit under the Poisson Hypothesis) matches Theorem 3.1, which proves that, as K→∞, the PH–GL dynamics converge in probability to the neural-field model (2.1) via an LLN for triangular arrays and spatial averaging assumptions . Part B (RMF ⇒ PH in the quadratic case with an O(M^{-1/2}) total-variation rate at each fixed time) matches Theorem 3.3, which explicitly states d_TV(λ^{M,K}_m(x,t), λ^K(x,t)) ≤ C(t)/√M for all m and x . The proof strategies differ: the paper uses a Chen–Stein bound plus a triangular LLN, with a thresholding device to handle quadratic growth , whereas the candidate outlines an alternative path via Efron–Stein variance control and thinning couplings. One minor quibble in the paper is the assertion (4.9) claiming existence of a deterministic threshold C such that, at fixed t, the truncated and original RMF dynamics coincide almost surely; the presented tail bound justifies approximation (and pathwise equality after stopping), not equality with probability one for a fixed finite C . This looks like a fixable presentation issue that does not undermine the theorems’ validity. Overall, the paper’s statements are correct, and the model’s solution is also correct but follows a different proof outline.