Author

Mickael Nahon

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Preprint Oct 2026

Zeros of the Spectrogram of White Noise with Hermite Windows

We study the zeros of the spectrogram of complex white noise analyzed with Hermite windows of order n, extending the classical Gaussian-window correspondence with Gaussian Analytic Functions to the polyanalytic setting. Using the polyanalytic Bargmann transform, these zeros split into two families according to the sign...

Charaf Bellourak, S. Meignen, K. Polisano et al. · 0 citations

Preprint Oct 2026

Shape optimisation of the maximum of the gradient of the torsion function on convex sets

We analyse the boundary behaviour of the gradient of the torsion function $w_\Om$ in convex domains $\Om\subset\mathbb{R}^d$. We prove that its $L^\infty$-norm is attained at a boundary point and establish the stability of this norm under general (convex) perturbations. For problems of the form $$\sup\{\|\nabla w_{\Om}...

M. J. Van den Berg, D. Bucur, Mickael Nahon · 0 citations

Preprint Sep 2026

Optimal regularity for vectorial, higher order and non-minimizing Bernoulli problems

We prove the Lipschitz regularity of solutions for a wide class of generalized Bernoulli free boundary problems, in vectorial, higher order, and non-minimizing settings. Our method does not rely on notions of viscosity solutions or comparison methods, which allows us to reach the optimal regularity for Bernoulli-type p...

G. De Philippis, Jonas Hirsch, Mickael Nahon · 1 citation