School of Mathematical Sciences

On links between the random operator and random matrix theories menu

On links between the random operator and random matrix theories

Speaker: 
Leonid Pastur (Kharkov)
Joint meeting with London Analysis and probability Seminar
Date/Time: 
Wed, 26/09/2012 - 17:00
Room: 
M203

We present several families of selfadjoint ergodic operators for which we prove that if the parameter indexing operators of a given family tends to infinity then their Integrated Density of States converges weakly to the infinite size limit of the Normalized Counting Measure of eigenvalues of certain random matrices. We then give an informal discussion of these results as possible indications of the presence of the continuous spectrum of the random ergodic operators belonging to considered families for sufficiently large values of the indexing parameters.