By Wolfgang König
This is a accomplished survey at the study at the parabolic Anderson
model – the warmth equation with random strength or the random stroll in random
potential – of the years 1990 – 2015. The research of this version requires
a mix of instruments from likelihood (large deviations, extreme-value
theory, e.g.) and research (spectral conception for the Laplace operator with
potential, variational research, e.g.). We clarify the historical past, the
applications, the questions and the connections with different types and formulate
the such a lot appropriate effects at the long-time habit of the answer, like quenched
and annealed asymptotics for the complete mass, intermittency, confinement and
concentration houses and mass move. in addition, we clarify the most
successful evidence tools and provides an inventory of open examine difficulties. Proofs are
not targeted, yet concisely defined and commented; the formulations of some
theorems are a little bit simplified for larger comprehension.
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Extra info for The Parabolic Anderson Model: Random Walk in Random Potential (Pathways in Mathematics)
The Parabolic Anderson Model: Random Walk in Random Potential (Pathways in Mathematics) by Wolfgang König