Determinantal transition kernels for some interacting particles on the line

TL;DR

This paper derives determinantal transition kernels for four Markovian interacting particle systems on the line, revealing their structure and connections to known kernels like Schutz's for TASEP, through intertwining with Karlin-McGregor kernels.

Contribution

It introduces new determinantal kernels for specific interacting particle systems by establishing their intertwining with Karlin-McGregor kernels, extending the understanding of their structure.

Findings

Kernels are determinantal and inherit structure from Karlin-McGregor formula.

Kernels are similar to Schutz's kernel for TASEP.

Intertwining techniques reveal connections between different particle systems.

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 Schutz's kernel for the totally asymmetric simple exclusion process.