2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209547We 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.ProbabilityMathematical Physicstext