Abstract:
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.
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