  In this paper, we study a particular deformation of the Jackiw-Teitelboim
gravity recently considered by Maxfield, Turiaci and independently by Witten.
We will compute the partition function of this model as well as its higher
order correlators to all orders in genus expansion in the low temperature limit
for small perturbations. In this limit, the results match with those obtained
from the Airy limit of a Hermitian random matrix ensemble. Using this result,
we will also study the free energy of the model. One observes that although the
annealed free energy has pathological behaviors, under certain assumptions, the
quenched free energy evaluated by replica trick exhibits the desired properties
at low temperatures.
