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Searches for primordial non-Gaussianity in cosmological perturbations are akey means of revealing novel primordial physics. However, robustly extractingsignatures of primordial non-Gaussianity from non-linear scales of thelate-time Universe is an open problem. In this paper, we apply k-NearestNeighbor cumulative distribution functions, kNN-CDFs, to the\textsc{quijote-png} simulations to explore the sensitivity of kNN-CDFs toprimordial non-Gaussianity. An interesting result is that for halo samples with$M_h<10^{14}$ M$_\odot$/h, the kNN-CDFs respond to \textit{equilateral} PNG ina manner distinct from the other parameters. This persists in the galaxycatalogs in redshift space and can be differentiated from the impact of galaxymodelling, at least within the halo occupation distribution (HOD) frameworkconsidered here. kNN-CDFs are related to counts-in-cells and, through mapping asubset of the kNN-CDF measurements into the count-in-cells picture, we showthat our results can be modeled analytically. A caveat of the analysis is thatwe only consider the HOD framework, including assembly bias. It will beinteresting to validate these results with other techniques for modeling thegalaxy--halo connection, e.g., (hybrid) effective field theory orsemi-analytical methods.

Small-scale signatures of primordial non-Gaussianity in k-Nearest Neighbour cumulative distribution functions