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

References in corpus (3)

• Orthogonal polynomial ensembles in probability theory
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates

Cited by in corpus (1)

• Large time asymptotics of growth models on space-like paths I: PushASEP