  We consider multiverse models in two-dimensional linear dilaton-gravity
theories as toy models of false vacuum eternal inflation. Coupling conformal
matter we calculate the Von Neumann entropy of subregions. When these are
sufficiently large we find that an island develops covering most of the rest of
the multiverse, leading to a Page-like transition. This resonates with a
description of multiverse models in semiclassical quantum cosmology, where a
measure for local predictions is given by saddle point geometries which
coarse-grain over any structure associated with eternal inflation beyond one's
patch.
