Stochastic particle dynamics on a lattice with Pfaffian correlations

In the first part of the talk I describe some known dynamical particle models (on a lattice and on a line), in particular, "nonintersecting paths" processes introduced by Karlin and McGregor in late 1950's. An important property of such models is that their certain n-point averages (namely, the space-time correlation functions) have the form of n x n determinants. In particular, this property provides a rather simple approach to studying various limit regimes of such stochastic processes.
In the second part I introduce a new interesting example of a stochastic particle dynamics on a lattice whose n-point space-time correlation functions have the form of 2n x 2n Pfaffians. This dynamics admits an unexpected description in terms of Karlin-McGregor's processes.