= Solution
Near a red giant's compact core, intense nuclear burning in a small region can produce a large $L_r/m_r$ and a steep required radiative gradient. Where this exceeds the adiabatic gradient, <convection> transports the released <energy> and mixes fuel. Core helium burning is a clear example: the strongly temperature-sensitive <Triple-alpha process> commonly produces a convective burning core; shell flashes can also make convective regions.https://doi.org/10.1051/0004-6361/201527171[helium-burning core convection and its temperature-sensitive energy source]{ref}
The qualification matters: an inert degenerate helium core and a steady hydrogen-burning shell on the first-ascent <red giant branch> are not universally convective; conduction or radiation may dominate there. Red giants also commonly have deep <convective envelopes>. \b[The physical condition is an excessive required radiative gradient, not proximity to the centre alone.]
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