Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures

The analogy between determinantal point processes (DPPs) and free fermionic calculi is well-known. We out that, from the perspective of algebras, Pfaffian (PfPPs) naturally emerge, show that a positive contraction acting on ''doubled'' one-particle space with an additional structure defines unique PfPP. Recently, Olshanski inverted direction fermions to DPPs, proposed scheme construct state quasi-invariant probability measure, introduced notion perfectness measure. propose method check Schur measures are perfect as long they under action symmetric group. also study conditional for PfPPs associated projection operators. Consequently, we again operators onto subspaces explicitly described.