  Sliding at a quasi-statically loaded frictional interface can occur via
macroscopic slip events, which nucleate locally before propagating as rupture
fronts very similar to fracture. We introduce a novel microscopic model of a
frictional interface that includes asperity-level disorder, elastic interaction
between local slip events, and inertia. For a perfectly flat and homogeneously
loaded interface, we find that slip is nucleated by avalanches of asperity
detachments of extension larger than a critical radius $A_c$ governed by a
Griffith criterion. We find that after slip, the density of asperities at a
local distance to yielding $x_\sigma$ presents a pseudo-gap $P(x_\sigma) \sim
(x_\sigma)^\theta$, where $\theta$ is a non-universal exponent that depends on
the statistics of the disorder. This result makes a link between friction and
the plasticity of amorphous materials where a pseudo-gap is also present. For
friction, we find that a consequence is that stick-slip is an extremely slowly
decaying finite size effect, while the slip nucleation radius $A_c$ diverges as
a $\theta$-dependent power law of the system size. We discuss how these
predictions can be tested experimentally.
