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Numerical simulations of a partially-premixed, turbulent jet diffusion flame stabilised in a hot vitiated co-flow are performed. For auto-igniting flames, an accurate prediction of flame stabilisation, which depends on a delicate balance between turbulent transport and chemical kinetics at the flame base, poses an enormous challenge to conventional turbulent combustion models. Multiple mapping conditioning/large eddy simulation (MMC-LES), a promising tool for modelling turbulence-chemistry interactions, has been successfully applied to simulate a variety of combustion applications involving gaseous, liquid, and solid fuels. MMC-LES is a full \gls{PDF} method where MMC plays the role of the mixing model, emulating molecular mixing phenomenon. MMC attempts to produce accurate molecular mixing by localising mixing in an independent, composition-like reference space. Due to this enforced localised mixing, a sparse distribution of stochastic Lagrangian particles for may be used for the Monte-Carlo simulation of the sub-grid joint-composition PDF equation. In the present study, we employ MMC-LES to investigate the auto-igniting methane/air flames of UC Berkeley. A sparse resolution of 1 particle per 10 Eulerian finite-volume cells is used in this study, which offers much cheaper computing expenses in comparison to the conventional transported PDF approach. A skeletal chemical mechanism, based on GRI 3.0, containing 30 species and 184 reactions, represents the oxidation of methane. The time-scale of molecular mixing is modelled using the recently published \textit{dyn-aISO} model to assess its performance in an auto-igniting configuration.