The Parabolic Anderson Model

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Focusing on the parabolic Anderson model, this survey explores research from 1990 to 2015, integrating probability and analysis tools. It covers the model's background, applications, and connections to other frameworks, detailing significant results regarding long-term solution behavior, including asymptotics, intermittency, and mass flow. Although proofs are not extensively detailed, they are summarized and clarified, with some theorems presented in a simplified manner. The book also highlights successful proof methods and outlines open research questions in the field.