##### Eigenvalue statistics for Schrödinger operators with random point interactions on $\mathbb{R}^d$, $d=1,2,3$
We prove that the local eigenvalue statistics at energy $E$ in the localization regime for Schr\"odinger operators with random point interactions on $\mathbb{R}^d$, for $d=1,2,3$, is a Poisson point process with the intensity measure given by the density of states at $E$ times the Lebesgue measure. This is one of the first examples of Poisson eigenvalue statistics for the localization regime of multi-dimensional random Schr\"odinger operators in the continuum. The special structure of resolvent of Schr\"odinger operators with point interactions facilitates the proof of the Minami estimate for these models.
###### NurtureToken New!

Token crowdsale for this paper ends in

###### Authors

Are you an author of this paper? Check the Twitter handle we have for you is correct.

###### Subcategories
-

#1. Which part of the paper did you read?

#2. The paper contains new data or analyses that is openly accessible?
#3. The conclusion is supported by the data and analyses?
#4. The conclusion is of scientific interest?
#5. The result is likely to lead to future research?

User:
Repo:
Stargazers:
0
Forks:
0
Open Issues:
0
Network:
0
Subscribers:
0
Language:
None
Views:
0
Likes:
0
Dislikes:
0
Favorites:
0
0
###### Other
Sample Sizes (N=):
Inserted:
Words Total:
Words Unique:
Source:
Abstract:
None
05/20/19 06:05PM
14,253
2,486
###### Tweets
MathPHYPapers: Eigenvalue statistics for Schr\"odinger operators with random point interactions on $\mathbb{R}^d$, $d=1,2,3$. https://t.co/VCA3HVvwC7
mathMPb: Peter D. Hislop, Werner Kirsch, M. Krishna : Eigenvalue statistics for Schrödinger operators with random point interactions on $\mathbb{R}^d$, $d=1,2,3$ https://t.co/9Ou4PCj15M https://t.co/lmlBiWd1zK