COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Probability > Local semicircle law and level repulsion for Wigner random matrices

## Local semicircle law and level repulsion for Wigner random matricesAdd to your list(s) Download to your calendar using vCal - Benjamin Schlein (Cambridge)
- Tuesday 10 February 2009, 14:00-15:00
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
If you have a question about this talk, please contact HoD Secretary, DPMMS. Consider ensembles of N by N hermitian random matrices with independent and identically distributed entries (up to the symmetry constraints), scaled so that the typical distance between successive eigenvalues is of the order 1/N. In this talk, I am going to discuss some properties of the spectrum of these matrices as N tends to infinity. In particular, I am going to present a proof of the validity of the semicircle law for the eigenvalue density on energy scales of the order K/N, in the limit of large but fixed K (independent of N). This is the smallest scale on which the semicircle law can be expected to hold. Moreover, I am going to discuss some upper bounds on the probability of finding eigenvalues in a given interval, which show the phenomenon of level repulsion. This is a joint work with L. Erdos and H.-T. Yau. This talk is part of the Probability series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS info aggregator
- DPMMS lists
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB
- Probability
- School of Physical Sciences
- Statistical Laboratory info aggregator
- bld31
Note that ex-directory lists are not shown. |
## Other listsMagdalene Society of Medievalists The Crisis of Democracy? Evidence from the Post-Communist World Mini Courses in Theoretical Computer Science## Other talksThe genetics of depression Deep & Heavy: Using machine learning for boosted resonance tagging and beyond Description: TIE proteins: chemical harpoons of Gram-positive bacteria The Ambonese Rumphius and his inter-island information networks Fundamental Limits to Volcanic Cooling and its Implications for Past Climate on Earth "Itsa me! Luigi!" [citation needed] - unlocking your referencing skills |