Title: ``Coalescence of geodesics and the BKS midpoint problem in first-passage percolation.'' Abstract: We consider first-passage percolation on Z^2 with independent and identically distributed weights. Under the assumption that the limit shape has at least 32 extreme points, we prove that…
Title: ``Free Probability for predicting the performance neural networks". Abstract: Gradient descent during the learning process of a neural network can be subject to many instabilities. The spectral density of the Jacobian is a key component for analyzing stability. Following…
Title: ``Method of Moments and Edge Eigenvalues.'' Abstract: The method of moments is a classical technique for showing weak convergence and follows a simple recipe: for any natural number m; compute the mth moments of the random variables of interest,…
Title: ``Metastable regimes of diffusion processes''. Abstract: I will discuss a classical example featuring a metastable behavior: finite-dimensional diffusion processes in the vanishing noise limit. Exponential estimates were introduced fifty years ago by Freidlin and Wentzell. Recent developments in potential…
Title: ``Non-equilibrium multi-scale analysis and coexistence in competing first-passage percolation.'' Abstract: We consider a natural random growth process with competition on Z^d called first-passage percolation in a hostile environment, that consists of two first-passage percolation processes FPP_1 and FPP_\lambda…
Title: ``Spin clusters in random triangulations coupled with Ising mode''. Abstract: We investigate geometric properties of random planar triangulations coupled with an Ising model. This model is known to undergo a combinatorial phase transition at an explicit critical temperature, for…
Title: ``Boundary correlations in planar LERW and UST.'' Abstract: We present explicit formulas for the probabilities of general boundary visit events for planar loop-erased random walks (LERW), as well as for connectivity events for branches in the uniform spanning tree…
Title: ``Unlinked monotone regression''. Abstract : We consider so-called univariate unlinked regression when the unknown regression curve is monotone. In standard monotone regression, one observes a pair (X;Y) where a response Y is linked to a covariate X through the…
Title: ``Approximately Hadamard matrices and random frames''. Abstract: An n by n matrix with plus-minus 1 entries which acts as a scaled isometry is called Hadamard. Such matrices exist in some, but not all dimensions. Combining number-theoretic and probabilistic tools…
Title: ``The Riemann zeta distribution.'' Abstract: We examine statistical properties of integers when they are sampled using the Riemann zeta distribution and compare to similar properties when they are sampled according to "uniform" or harmonic distributions. For example, as the…
Title: ``Strong convergence of tensor products of independent GUE matrices.'' Abstract: Given tuples of properly normalized independent NxN GUE matrices (X_1,...,X_r) and (Y_1,...,Y_s), we proved that the tuple (X_1⊗I,...,X_r⊗I,I⊗Y_1,...,I⊗Y_s) of matrices converges strongly as N tends to infinity. We will…
Title: ``Measuring shapes with random Delaunay mosaics.'' Abstract: Classically, we are used to working with shapes embedded into the square lattice. It might be anything, a pixelated photo of a maple leaf, or a 3d-scanned voxelated image of a human…