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.
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