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 > Isaac Newton Institute Seminar Series > Characterstic polynomials of random matrices and logarithmically correlated processes

## Characterstic polynomials of random matrices and logarithmically correlated processesAdd to your list(s) Download to your calendar using vCal - Fyodorov, Y (Queen Mary, University of London)
- Thursday 23 April 2015, 10:00-11:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact webseminars. Random Geometry I will discuss relations between logarithmically-correlated Gaussian processes and the characteristic polynomials of large random $N imes N$ matrices, either from the Circular Unitary (CUE) or from the Gaussian Unitary (GUE) ensembles. Such relations help to address the problem of characterising the distribution of the global maximum of the modulus of such polynomials, and of the Riemann $zetaleft(rac{1}{2}+it ight)$ over some intervals of $t$ containing of the order of $log{t}$ zeroes. I will show how to arrive to an explicit expression for the asymptotic probability density of the maximum by combining the rigorous Fisher-Hartwig asymptotics with the heuristic {it freezing transition} scenario for logarithmically correlated processes. Although the general idea behind the method is the same for both CUE and GUE , the latter case is much more technically challenging. In particular I will show how the conjectured {it self-duality} in the freezing transition scenario plays the crucial role in selecting the form of the maximum distribution for GUE case. The found probability densities will be compared to the results of direct numerical simulations of the maxima. The presentation is mainly based on joint works with Ghaith Hiary, Jon Keating, Boris Khoruzhenko, and Nick Simm. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
- bld31
Note that ex-directory lists are not shown. |
## Other listsInteresting talks- 1st try Faculty of Music Colloquia High dimensional statistics## Other talksBuilding cortical networks: from molecules to function Improving on Nature: Biotechnology and the Ethics of Animal Enhancement CANCELLED DUE TO STRIKE ACTION Nonlinear nonmodal stability theory Changing languages in European Higher Education: from official policies to unofficial classroom practices Numerical solution of the radiative transfer equation with a posteriori error bounds |