The Parabolic Anderson Model Random Walk in Random Potential /

• Main Author: König, Wolfgang (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
• Series: Pathways in Mathematics,
• Subjects: Mathematics.; Mathematical physics.; Probabilities.; Physics.; Probability Theory and Stochastic Processes.; Mathematical Applications in the Physical Sciences.; Mathematical Methods in Physics.

This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-valu...

Table of Contents:

• 1 Background, model and questions
• 2 Tools and concepts
• 3 Moment asymptotics for the total mass
• 4 Some proof techniques
• 5 Almost sure asymptotics for the total mass
• 6 Strong intermittency
• 7 Refined questions
• 8 Time-dependent potentials.