Author

Jaume de Dios Pont

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Preprint Aug 2026

Counterexamples to Schiffer's Conjecture

The Schiffer conjecture states that if a smooth domain $\Omega \subset \mathbb{R}^n$ admits a Neumann eigenfunction of the Laplacian which is constant at the boundary, then the domain is a ball. It is intimately related to Pompeiu's problem, stating that if a nonzero function integrates zero over any rigid motion of $\...

G. Cao-Labora, Jaume de Dios Pont · 3 citations

Preprint Jun 2026

Geometric Dyson Brownian Motions and the Free Log-Normal Limit for a Non-Square Gaussian Matrix Product

We study the squared singular value spectrum of a non-square product of independent real Gaussian matrices, equivalently the feature covariance spectrum of a deep linear neural network at initialization. Starting from the fixed-$m$ covariance diffusion previously obtained in the proportional depth-width limit, we recor...

Mufan Bill Li, Jaume de Dios Pont, M. Nica et al. · 0 citations