The zero-intelligence (ZI) model (Gode–Sunder 1993, Farmer et al. 2005): orders arrive randomly, cancel randomly. Despite no agent intelligence, the LOB generates realistic spread, price impact, and volume profiles.
Cont–Stoikov–Talreja 2010: analytic solution for the stationary distribution of the LOB. The spread S ~ (μ/λ)^{1/2}·(δ/λ)^{1/4} — market orders thin the book, cancellations and limit orders replenish it.