Text

The Parabolic Anderson Model: Random Walk in Random Potential

---

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-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.

---

Availability

No copy data

Detail Information

Series Title

Pathways in Mathematics

Call Number

-

Publisher

Cham : Birkhäuser Cham., 2016

Collation

XI, 192

Language

English

ISBN/ISSN

978-3-319-33596-4

Classification

NONE

Content Type

text

Media Type

computer

Carrier Type

-

Edition

-

Subject(s)

Mathematical Methods in Physics

Specific Detail Info

-

Statement of Responsibility

Wolfgang König

Other Information

Cataloger

Jemadi

Source

https://link.springer.com/content/pdf/10.1007/978-3-319-33596-4.pdf?pdf=button

Validator

-

Other version/related

File Attachment

Comments

---

You must be logged in to post a comment