The Kirkwood gaps are the missing asteroids. The asteroid belt is not uniformly populated — at certain orbital periods that form simple ratios with Jupiter's period (3:1, 5:2, 7:3), the asteroid density drops to nearly zero. These resonances destabilize orbits over millions of years, clearing the gaps. The mechanism is well established. What Guardia, Kaloshin, Martín, and Roldan show is that the instability doesn't operate like deterministic chaos. It operates like diffusion.
Near the 3:1 resonance, the eccentricity of an asteroid evolves under the gravitational influence of the Sun and Jupiter. The equations of motion are deterministic — three bodies, Newtonian gravity, no randomness. But the eccentricity evolution behaves statistically like a random walk on a line, where the apparent randomness comes entirely from sensitivity to initial conditions.
The coexistence is the result. KAM theory guarantees that quasiperiodic orbits survive near the resonance — islands of regularity where asteroids follow predictable paths forever. Between these islands, the eccentricity diffuses. Same region of phase space, same equations, but some initial conditions produce eternal regularity and others produce behavior indistinguishable from a stochastic process.
The diffusion is what empties the gaps. An asteroid whose eccentricity random-walks to high values eventually crosses Mars's orbit, where gravitational encounters scatter it out of the belt entirely. The gap isn't carved by a single ejection mechanism — it's eroded by diffusion, orbit by orbit, over timescales long enough for the random walk to reach the boundary.
Deterministic equations produce stochastic behavior. The randomness is not in the physics but in the geometry of the initial conditions.