Abstract Understanding the ignition of combustible mixtures by hot jets of burnt gases plays an important role in explosion protection. In this work a PDF method in conjunction with a reaction–diffusion manifold (REDIM) is used to investigate the ignition of a hydrogen/air mixture by a hot turbulent jet. In accordance with experimental results it is observed in numerical investigations that after an ignition delay time, the ignition is typically initiated at the jet head vortex. The scope of the current work is to investigate the mechanisms leading to ignition and explain the processes governing the ignition delay time as well as the ignition location. It is shown that macro- as well as micromixing and the chemical kinetics have a profound influence on the ignition process and that a realistic model for the ignition process has to account for all these processes in combination with a transient description of the jet penetration.