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.
“A visible feature of the book is its emphasis on the tool and idea development. … The book is particularly beneficial to the following two groups’ of readers: (1) Those who have been working in the direction of PAM or related areas … (2) Young researchers who are considering starting their work in this direction. … Remarks and examples are distributed throughout the entire book with historic accounts and specific discussions, which further increases the readability of the book.” (Xia Chen,Mathematical Reviews, June, 2017)
Innehållsförteckning
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.
Andrea Back, Jörg Becker, Wolfgang König, Hermann Krallmann, Bodo Rieger, August-Wilhelm Scheer, Dietrich Seibt, Peter Stahlknecht, Horst Strunz, Rainer Thome, Hartmut Wedekind