Cosmic Himalayas in CROCODILE: Probing the Extreme Quasar Overdensities by Count-in-cells Analysis and Nearest-neighbor Distribution

Abstract

The recently reported Cosmic Himalayas (CH)—an extreme quasar overdensity at z  ∼ 2—poses an apparent challenge to the Lambda cold dark matter (ΛCDM) framework, with a reported significance of δ  = 16.9 σ under Gaussian assumptions. Such an event appears improbably rare, with a formal probability of P  ∼ 10 −68 . In this work, we investigate whether CH-like structures can naturally arise in cosmological hydrodynamic simulations. Using the CROCODILE simulation, which self-consistently models galaxy–black hole coevolution, we examine quasar clustering through two complementary approaches: the count-in-cells (CIC) statistic, which probes large-scale overdensities, and the nearest-neighbor distribution (NND), sensitive to small-scale environments. CIC analysis reveals that the underlying distribution is heavy-tailed and non-Gaussian, and that conventional Gaussian-based evaluation substantially overestimates the significance of extreme events. When modeled with an asymmetric generalized normal distribution (AGND), the inferred rarity of the CH is substantially reduced and reconciled with standard ΛCDM; for instance, regions appearing as 12 σ Gauss outliers under Gaussian assumptions ( P  ∼ 10 −33 ) are found to occur in AGND regimes with a probability of P  ∼ 10 −4 . NND analysis further demonstrates that extreme overdense regions within the simulation can naturally sustain two-point correlation function values similar to those observed in the CH ( r 0 eff ≃ 30 h − 1 Mpc ), suggesting that the strong clustering stems from sample selection biases and local environmental variations. These two analyses conclusively highlight the importance of adopting non-Gaussian statistics when quantifying extreme overdensities of quasars and establish that the CH is not an anomaly, but a natural outcome of structure formation in the ΛCDM universe.