  A large class of two-dimensional dilaton-gravity theories in asymptotically
AdS$_2$ spacetimes are holographically dual to a matrix integral, interpreted
as an ensemble average over Hamiltonians. Viewing these theories as
Jackiw-Teitelboim gravity with a gas of defects, we extend this duality to a
broader class of dilaton potentials compared to previous work by including
conical defects with small deficit angles. In order to do this we show that
these theories are equal to the large $p$ limit of a natural deformation of the
$(2,p)$ minimal string theory.
