  We derive the local statistics of the canonical ensemble of free fermions in
a quadratic potential well at finite temperature, as the particle number
approaches infinity. This free fermion model is equivalent to a random matrix
model proposed by Moshe, Neuberger and Shapiro. Limiting behaviors obtained
before for the grand canonical ensemble are observed in the canonical ensemble:
We have at the edge the phase transition from the Tracy--Widom distribution to
the Gumbel distribution via the Kardar-Parisi-Zhang (KPZ) crossover
distribution, and in the bulk the phase transition from the sine point process
to the Poisson point process. A similarity between this model and a class of
models in the KPZ universality class is explained. We also derive the
multi-time correlation functions and the multi-time gap probability formulas
for the free fermions along the imaginary time.
