Constraining the galaxy-halo connection at $z>10$ using the neighbors of UV-bright galaxies
JWST has discovered an overabundance of UV-luminous galaxies compared to extrapolations from pre-JWST galaxy formation models. Distinguishing between proposed theoretical explanations requires constraining the halo masses of these systems, which can be probed through clustering. However, at $z>10$, low galaxy number densities render traditional clustering measurements challenging. We introduce a novel formalism that uses information about the local environments ($\lesssim$2 arcmin) of individual UV-bright galaxies at $z>10$ to test the galaxy-halo connection implied by theoretical models for the UVLF excess. We create mock JWST observations using (500 cMpc)$^3$ 21cmFAST simulations to forward-model the spatial distribution of fainter photometric candidates around UV-bright galaxies. We find that the distance to the nearest neighbor is sensitive to the stochasticity of the UV luminosity-halo mass relation, and can distinguish between models where UV luminosity is boosted uniformly in galaxies versus models with high stochasticity in UV luminosity at fixed halo mass. As a proof-of-concept, we apply our framework to observations around the two brightest confirmed galaxies at $z>10$, GN-z11 and JADES-GS-z14-0, and find that the lack of neighbors within $<0.5$ arcmin of these sources disfavors models where UV luminosity is boosted uniformly, suggesting that stochasticity is important for explaining their high UV luminosities. We forecast that distinguishing between these models at high significance requires deep imaging surveying $<1.1$ arcmin around $7$-$15$ bright galaxies ($M_{\rm UV}\lesssim-21$) at $z =10$-$12$, dropping to $\lesssim5$ at $z\sim14$, capable of detecting their neighbors down to $M_{\rm UV,lim}\approx-18$. These observations are within reach of JWST, Roman and Euclid surveys, providing a path to constraining the galaxy-halo connection at our redshift frontier.