# Monday programme

**Room B3.03**

**Morning Session Chair: Gernot Akemann**

**Afternoon Session Chair: Mario Kieburg**

Time |
Speaker |
Title |
Abstract |

10:00-10:55 |
Coffee in the Common Room |
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10:55-11:00 |
Welcome from organisers |
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11:00-11:50 |
Arno Kuijlaars | Propagation of singular behavior in UE and GUE sums |
I will discuss sums of Hermitian random matrices $M + \sqrt{\tau} H$ |

11:50-12:40 |
Pierpaolo Vivo | Universal fluctuation formulae for one-cut β-ensembles - with a combinatorial touch | I discuss a recently obtained analytical formula for the covariance Cov(A,B) of two smooth linear statistics on the eigenvalues of a one-cut β-ensemble of random matrices. This allows to compute the generating function of the covariances of power traces for one-cut β-ensembles of random matrices in the limit of large matrix size. This formula depends only on the support of the spectral density, and is therefore universal for a large class of models. I briefly discuss the connection with the combinatorial problem of non-crossing pairings of 2 circles with ‘k’ and ‘l’ points on them, respectively.
In collaboration with Francesco Mezzadri and Fabio Deelan Cunden [J. Phys. A: Math. Theor. 48, 315204 (2015); Phys. Rev. Lett. 113, 070202 (2014)] |

12:40-14:10 |
Lunch in the Common Room |
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14:10-15:00 |
Khanh Duy Trinh | On spectral measures of beta ensembles |
This talk concerns with the limiting behaviour of spectral measures of random Jacobi matrices of Gaussian, Wishart and MANOVA beta ensembles. We show that the spectral measures converge weakly to a limit distribution which is the semicircle distribution, Marchenko-Pastur distributions or the arcsine distribution, respectively. Regarding that |

15:00-16:00 |
Tea in the Common Room |
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16:00-16:50 |
Chris Joyner |
The probability distribution of spectral moments for the Gaussian beta-ensembles |
We derive the joint probability distribution of the first two spectral moments for the Gaussian beta-Ensembles random matrix ensembles in N dimensions for any N. This is achieved by mak-ing use of two complementary invariants of the domain where the spectral moments are de-fined. Our approach is significantly different from those employed previously to answer related questions and potentially offers new insights. We also discuss the problems faced when at-tempting to include higher spectral moments. This is work together with U. Smilansky and T. Maciazek |

18:00-20:00 |
Dinner in the Common Room |