The parabolic Anderson model
W König, T Wolff - Preprint. Available at www. wiasberlin. de/people …, 2015 - Springer
This is a survey of the parabolic Anderson model (PAM), the Cauchy problem for the heat
equation with random potential. This model and many variants and related models are …
equation with random potential. This model and many variants and related models are …
Stochastic analysis and random Schrödinger operators
N Ueki - Sugaku Expositions, 2018 - ams.org
The Donsker-Varadhan theory on large deviations [12] and the Malliavin calculus [43] are
the main theories in the stochastic analysis founded in the latter twentieth century. Among …
the main theories in the stochastic analysis founded in the latter twentieth century. Among …
Details About Intermittency
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
In this chapter, we discuss much stronger and more detailed assertions about intermittency
than we did before. They characterise the long-time behaviour of the mass flow through a …
than we did before. They characterise the long-time behaviour of the mass flow through a …
Some Proof Techniques
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
Abstract In Sect. 3.2, we described the heuristics for the large-t exponential rate of the
moments of the total mass U (t), neglecting all technical issues. More precisely, we only gave …
moments of the total mass U (t), neglecting all technical issues. More precisely, we only gave …
Tools and Concepts
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
One of the most interesting features of the PAM is that, being a partial differential equation
with random coefficients, it lies in the intersection of probability and functional analysis …
with random coefficients, it lies in the intersection of probability and functional analysis …
Almost Sure Asymptotics for the Total Mass
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
In this section, we explain the basic picture that underlies the almost sure asymptotics of the
total mass U (t) under Assumption (H). Like for the moments, we will give an argument only …
total mass U (t) under Assumption (H). Like for the moments, we will give an argument only …
Background, Model and Questions
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
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Time-Dependent Potentials
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
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Refined Questions
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
Let us survey a number of questions around the PAM that go beyond the basic questions
that we have treated so far. In Sect. 7.1 we show what refined techniques can say about …
that we have treated so far. In Sect. 7.1 we show what refined techniques can say about …
Moment Asymptotics for the Total Mass
W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
In this chapter, we explain what the asymptotics of the logarithm of the moments of the total
mass U (t) of the solution u (t,⋅) of the PAM in (1.1)–(1.2) are determined by, and how they …
mass U (t) of the solution u (t,⋅) of the PAM in (1.1)–(1.2) are determined by, and how they …