Multifractals, Mumford curves, and Eternal Inflation

We relate the Eternal Symmetree model of Harlow, Shenker, Stanford, and Susskind to constructions of stochastic processes arising from quantum statistical mechanical systems on Cuntz–Krieger algebras. We extend the eternal inflation model from the Bruhat–Tits tree to quotients by p-adic Schottky groups, again using quantum statistical mechanics on graph algebras.