This semester, we are meeting on Thursdays in the Seminar Room 4206 French Hall. Please email yizao.wang@uc.edu
if you want to be added to our email list or have any questions.
 Sep 14, Robbie Buckingham. Nonintersecting Brownian motions on the unit circle with drift.
 Sep 21, Joseph Najnudel. On Unitarily Invariant Random Infinite Hermitian Matrices.
 Oct 5, Valentin Bahier, Institut de Mathématiques de Toulouse, Spectrum of random permutation matrices on a microscopic scale.
In this talk we will focus on eigenvalues of random permutation matrices at a microscopic scale. First, we will see how a limiting point process naturally arises from the counting function of eigenvalues. Then, we will introduce a convenient coupling to investigate the behaviour of this point process, involving a scaleinvariant Poisson process on $(0,\infty)$. Finally, we will say a few words on related results for modified permutation matrices.
 Oct 26, Maylis Varvenne, Institut de Mathématiques de Toulouse, Rate of convergence to equilibrium for discretetime stochastic dynamics with memory.
We are interested in a general class of recursive discrete dynamics: $X_{n+1}=F(X_n,\delta_{n+1})$ where $(\delta_n)_{n\in\mathbb Z}$ is an ergodic stationary Gaussian sequence. We can think for instance of fractional Brownian motion increments. First, we will see how it is possible to define invariant distributions in this a priori nonMarkovian setting. Then, after proving existence of such a distribution, we will get a uniqueness result and a rate of convergence to this invariant distribution in total variation distance. The proof is based on a coupling method (with a step which is specific to this nonMarkovian framework) first implemented by M.Hairer in a continuous time setting. This method was also used by J. Fontbona and F. Panloup, as well as A. Deya, F. Panloup and S. Tindel in order to extend M. Hairer's results.
Past Seminar Archives (with photos!!)
Past Probability Events at UC
Other Probability Conferences
