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.Comment: 19 pages, LaTeX, 4 pdf figure