Title: ``Stopping sets and phase transitions on the Poisson space'' Abstract: I will discuss several refinements of the Poincaré inequality on the Poisson space, based on the use of "restricted hypercontractivity", stopping sets and continuous-time decision trees. One of the…
Title: ``Biparental genealogy'' Abstract: This is a joint work with Camille Coron. In the context of the biparental Moran model, we study the asymptotic distribution of ancestors weights in the population, by letting successively time and population size grow to…
Title : ``Sampling rates for l1-synthesis'' Abstract : This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the l1-synthesis basis pursuit allows to simultaneously estimate a coefficient…
Title: ``A modified bootstrap percolation on a random graph coupled with a lattice'' Abstract: A random graph model $G_{\mathbb{Z}^2_N,p_d}$ will be introduced, which is a combination of fixed torus grid edges in $(\mathbb{Z}/N \mathbb{Z})^2$ and some additional random ones.…
Title: ``The Breuer-Major theorem: old and new'' Abstract: The celebrated Breuer-Major theorem is a central limit theorem for a sum of elements of the form f(X_k), where f:R-->R is a given function and X is a Gaussian stationary sequence…
Title: ``Random matrix products: limit theorems and stationary measures''. Abstract: Random matrix products theory has known deep contributions in the last few years due to its large spectrum of applications: expander graphs, geometric group theory, diophantine approximation... Roughly speaking, its goal…
Title: ``The Aldous--Lyons conjecture on recurrent unimodular random graphs''. Abstract: This talk is concerned with the geometry of the (wired) Uniform Spanning Tree (UST) on an infinite graph, and in particular with a property called one-endedness, which says that…
Title: ``Dynamical entanglement and localization in disordered oscillator systems''. Abstract: Many-body localization (MBL) is the analogue of Anderson localization for large quantum systems when both disorder and interactions are present. Many-body localized systems do not thermalize under their own…
Title: ``An introduction to elementary Percolation Theory and some related processes.'' Abstract: I will give an introduction to the basic elements of Percolation Theory, including some motivations, basic inequalities and elementary properties. We will also briefly touch upon bootstrap…
Title: ``Random menhirs in a Poisson desert'' Abstract: ``The Voronoi diagram in desert areas of a Poisson process gives rise to very elongated cells whose convergence we study after suitable renormalization. (Joint work with Pierre Calka and Yann Demichel).''
Title: ``On the real Davies' conjecture'' Abstract: We show that every nxn matrix A is at least h-close to a real nxn matrix A+E whose eigenvectors have condition number at most O(1/h). In fact, we prove that, with high probability,…
Title: ``Modewise methods for tensor compression and recovery'' Abstract: Among the most widely used random matrix measurement models are (a) independent sub-gaussian models and (b) randomized Fourier-based models, allowing for the efficient computation of the measurements. My talk will be…