  We revisit the periodic Schur process introduced by Borodin in 2007. Our
contribution is threefold. First, we provide a new simpler derivation of its
correlation functions via the free fermion formalism. In particular, we shall
see that the process becomes determinantal by passing to the grand canonical
ensemble, which gives a physical explanation to Borodin's "shift-mixing" trick.
Second, we consider the edge scaling limit in the simplest nontrivial case,
corresponding to a deformation of the poissonized Plancherel measure on
partitions. We show that the edge behavior is described, in a certain crossover
regime different from that for the bulk, by the universal finite-temperature
Airy kernel, which was previously encountered by Johansson and Le Doussal et
al. in other models, and whose extreme value statistics interpolates between
the Tracy-Widom GUE and the Gumbel distributions. We also define and prove
convergence for a stationary extension of our model. Finally, we compute the
correlation functions for a variant of the periodic Schur process involving
strict partitions, Schur's P and Q functions, and neutral fermions.
