  We carried out an extensive analysis of the stability of the outer solar
system, making use of the frequency analysis technique over short-term
integrations of nearly a hundred thousand test particles, as well as a
statistical analysis of 200, 1 Gyr long numerical simulations, which consider
the mutual perturbations of the giant planets and the 34 largest
trans-Neptunian objects (we have called all 34 objects ``dwarf planets'', DPs,
even if probably only the largest of them are true DPs).
  From the frequency analysis we produced statistical diffusion maps for a wide
region of the $a$-$e$ phase-space plane; we also present the average diffusion
time for orbits as a function of perihelion. We later turned our attention to
the 34 DPs making an individualized analysis for each of them and producing a
first approximation of their future stability.
  From the 200 distinct realizations of the orbital evolution of the 34 DPs, we
classified the sample into three categories including 17 Stable, 11 Unstable,
and 6 Resonant objects each; we also found that statistically, 2 objects from
the sample will leave the trans-Neptunian region within the next Gyr, most
likely being ejected from the solar system, but with a non-negligible
probability of going inside the orbit of Neptune, either to collide with a
giant planet or even falling to the inner solar system, where our simulations
are no longer able to resolve their continuous evolution.
