Eynard-Mehta theorem, Schur process, and their pfaffian analogs
  We give simple linear algebraic proofs of Eynard-Mehta theorem, Okounkov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also discuss certain general properties of the spaces of all determinantal and Pfaffian processes on a given finite set. 
Alexei Borodin and Eric M. Rains