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 - Nachmias, A (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 Mustapha Amrani. 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:Note that ex-directory lists are not shown. |
## Other listsThe influence of signal strength on the differentiation of effector and memory T cells jer64's list Pembroke Papers Sequencing Workshop Infant Sorrow Arcadia Lectures## Other talksOptimising the definition of MR-based lung imaging biomarkers Can land rights prevent deforestation? Evidence from a large-scale titling policy in the Brazilian Amazon. CGHR Practitioner Series: Sharath Srinivasan, Africa's Voices HE@Cam Seminar: Christian Hill - Patient Access Scheme, Managed Access Agreements and their influence on the approval trends on new medicines, devices and diagnostics Carers and Careers: The Impact of Caring on Academic Careers |