Lifshits tails in the hierarchical Anderson model

Published 24 Jan 2011 in math-ph, math.MP, and math.SP | (1101.4468v3)

Abstract: We prove that the homogeneous hierarchical Anderson model exhibits a Lifshits tail at the upper edge of its spectrum. The Lifshits exponent is given in terms of the spectral dimension of the homogeneous hierarchical structure. Our approach is based on Dirichlet-Neumann bracketing for the hierarchical Laplacian and a large-deviation argument.

Abstract PDF Upgrade to Chat

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Create Your Own

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Top Community Prompts

Explain it Like I'm 14

Practical Applications

Conceptual Simplification

Sign Up to Activate View All Prompts

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (2)

Collections

Sign up for free to add this paper to one or more collections.