This is a entire survey at the learn at the parabolic Anderson version – the warmth equation with random power or the random stroll in random capability – of the years 1990 – 2015. The research of this version calls for a mixture of instruments from likelihood (large deviations, extreme-value idea, e.g.) and research (spectral thought for the Laplace operator with strength, variational research, e.g.). We clarify the historical past, the purposes, the questions and the connections with different types and formulate the main proper effects at the long-time habit of the answer, like quenched and annealed asymptotics for the complete mass, intermittency, confinement and focus homes and mass movement. additionally, we clarify the main profitable facts equipment and provides a listing of open learn difficulties. Proofs usually are not distinctive, yet concisely defined and commented; the formulations of a few theorems are a little simplified for larger comprehension.
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