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We study the relationship between dark-matter haloes and matter in the MIP$N$-body simulation ensemble, which allows precision measurements of thisrelationship, even deeply into voids. What enables this is a lack ofdiscreteness, stochasticity, and exclusion, achieved by averaging over hundredsof possible sets of initial small-scale modes, while holding fixed large-scalemodes that give the cosmic web. We find (i) that dark-matter-halo formation isgreatly suppressed in voids; there is an exponential downturn at low densitiesin the otherwise power-law matter-to-halo density bias function. Thus, therarity of haloes in voids is akin to the rarity of the largest clusters, andtheir abundance is quite sensitive to cosmological parameters. The exponentialdownturn appears both in an excursion-set model, and in a model in whichfluctuations evolve in voids as in an open universe with an effective$\Omega_m$ proportional to a large-scale density. We also find that (ii) haloestypically populate the average halo-density field in a super-Poisson way, i.e.with a variance exceeding the mean; and (iii) the rank-order-Gaussianized haloand dark-matter fields are impressively similar in Fourier space. We compareboth their power spectra and cross-correlation, supporting the conclusion thatone is roughly a strictly-increasing mapping of the other. The MIP ensembleespecially reveals how halo abundance varies with `environmental' quantitiesbeyond the local matter density; (iv) we find a visual suggestion that at fixedmatter density, filaments are more populated by haloes than clusters.

A halo bias function measured deeply into voids without stochasticity