7 papers
On the Banach--Mazur radius of
Omer Friedland, Assaf Naor, Pierre Youssef
We prove that any -dimensional normed space is at Banach--Mazur distance from .
On the Stability of the Jacobian Matrix in Deep Neural Networks
Benjamin Dadoun, Soufiane Hayou, Hanan Salam +2
Deep neural networks are known to suffer from exploding or vanishing gradients as depth increases, a phenomenon closely tied to the spectral behavior of the input-output Jacobian.…
Log-Sobolev under random monotone censoring
Patrick Oliveira Santos, Raghavendra Tripathi, Pierre Youssef
We show that the logarithmic Sobolev inequality of the Boolean cube is stable under random monotone censoring. More precisely, if is chosen uniformly among…
A note on quantum expanders
Cécilia Lancien, Pierre Youssef
We prove that a wide class of random quantum channels with few Kraus operators, sampled as random matrices with some sparsity and moment assumptions, typically exhibit a large spec…
Khintchine inequalities, trace monoids and Turán-type problems
Patrick Oliveira Santos, Raghavendra Tripathi, Pierre Youssef
We prove scalar and operator-valued Khintchine inequalities for mixtures of free and tensor-independent semicircle variables, interpolating between classical and free Khintchine-ty…
Central limit theorem for -independent products and higher-order tensors
Guillaume Cébron, Patrick Oliveira Santos, Pierre Youssef
We establish a central limit theorem (CLT) for families of products of -independent random variables. We utilize graphon limits to encode the evolution of independence and char…