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…
Title: ``Products of random transfer matrices and the statistical mechanics of disordered systems'' Abstract: The talk will focus on the top Lyapunov exponent of the transfer matrix for the nearest neighbor Ising chain with random external field. This Lyapunov exponent…
Title: ``Stationary measures on projective spaces under block-Lyapunov domination'' Abstract: A probability measure on the general linear group of d*d-invertible matrices induces a non-commutative random walk on this group and a Markov chain on the projective space of R^d. The…
Title : ``Recurrent Neural Networks and Ordinary Differential Equations'' Abstract : Deep learning has become a prominent method for many applications, for instance computer vision or neural language processing. Mathematical understanding of these methods is yet incomplete. A recent approach has been…
Title: ``Existence of absolutely continuous spectrum for random trees.'' Abstract: We establish a quantitative criterion for an operator defined on a Galton-Watson random tree for having an absolutely continuous spectrum. For the adjacency operator, this criterion requires that the offspring…
Title:``Large deviations for random walks without moment conditions on hyperbolic spaces''.Abstract: Consider a random walk on a hyperbolic space (the talk will mostly focuss on the special case of trees). It is known that the walk is converging almost surely…
Title: ``Quantum expander graphs'' Abstract: The goal of the talk will be to understand what quantum expander graphs are, what they are useful for, and how they can be constructed. We will first recall the definition of classical expander…
Title: ``An elementary proof of phase transition in the planar XY model''. Abstract: Using elementary methods we obtain a power-law lower bound on the two-point function of the planar XY spin model at low temperatures. This was famously first…
Title: ``Ising model with various perturbations''. Abstract: We consider the behavior of the critical Ising model under various perturbations. In two dimensions, we focus on the particle masses associated with the near-critical scaling limit of the model with an external…
Title: ``On the massive loop-erased random walks and massive SLEs''. Abstract: The last decade has witnessed numerous breakthroughs in establishing rigorously the conformal invariance of some statistical models at the critical temperature, largely due to the introduction of SLEs, Schramm…
Title: ``Some Insights from Neural Networks with Infinite Number of Parameters.'' Abstract: The theoretical analysis of infinite-width neural networks has led to many interesting practical results (choice of initialization schemes, choice of Bayesian priors etc.). However, the traditional infinite-width framework focuses…
Title: ``Log-Sobolev inequality for near-critical Ising models''. Abstract: For ferromagnetic Ising models, we show that the log-Sobolev constant satisfies a simple bound expressed only in terms of the susceptibility of the model. This bound implies very generally that the log-Sobolev…