# Moment Asymptotics for the Total Mass

• Wolfgang König
Chapter
Part of the Pathways in Mathematics book series (PATHMATH)

## Abstract

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 ()– () are determined by, and how they can be described. This is fundamental for a deeper study of the PAM, and we will develop a rich picture. We will be working under the basic assumption that $$(\xi (z))_{z\in \mathbb{Z}^{d}}$$ is an i.i.d. random potential and that all positive exponential moments of $$\xi (0)$$ are finite, in which case all the moments of U(t) are finite.

## Keywords

Principal Eigenvalue Poisson Point Process Random Potential Cumulant Generate Function Characteristic Formula
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer International Publishing Switzerland 2016

## Authors and Affiliations

• Wolfgang König
• 1
• 2
1. 1.für Angewandte Analysis und StochastikWeierstraß-InstitutBerlinGermany
2. 2.Institute for MathematicsTU BerlinBerlinGermany