  The dynamical stability of tightly packed exoplanetary systems remains poorly
understood. While for a two-planet system a sharp stability boundary exists,
numerical simulations of three and more planet systems show that they can
experience instability on timescales up to billions of years. Moreover, an
exponential trend between the planet orbital separation measured in units of
Hill radii and the survival time has been reported. While these findings have
been observed in numerous numerical simulations, little is known of the actual
mechanism leading to instability. Contrary to a constant diffusion process,
planetary systems seem to remain dynamically quiescent for most of their
lifetime before a very short unstable phase. In this work, we show how the slow
chaotic diffusion due to the overlap of three-body resonances dominates the
timescale leading to the instability for initially coplanar and circular
orbits. While the last instability phase is related to scattering due to
two-planet mean motion resonances (MMR), for circular orbits the two-planets
MMR are too far separated to destabilize systems initially away from them. We
develop an analytical model to generalize the empirical trend obtained for
equal mass and equally-spaced planets to general systems. We obtain an
analytical estimate of the survival time consistent with simulations over four
orders of magnitude for the planet to star mass ratio $\epsilon$, and 6 to 8
orders of magnitude for the instability time. We also confirm that measuring
the orbital spacing in terms of Hill radii is not adapted and that the right
spacing unit scales as $\epsilon^{1/4}$. We predict that beyond a certain
spacing, the three-planet resonances are not overlapped, which results in an
increase of the survival time. We finally discuss the extension of our result
to more general systems, containing more planets on initially non circular
orbits.
