Determinantal transition kernels for some interacting particles on the line

Abstract

We find the transition kernels for four Markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin-McGregor-type kernel. The resulting kernels all inherit the determinantal structure from the Karlin-McGregor formula, and have a similar form to Schiitz's kernel for the totally asymmetric simple exclusion process. © Association des Publications de l'Institut Henri Poincaré, 2008.