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Vanessa Piccolo

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Open access Oct 2026

Topological complexity of spiked random polynomials and finite-rank spherical integrals

We study the annealed complexity of Gaussian random homogeneous polynomials on the (N−1)-dimensional unit sphere in the presence of deterministic perturbations depending on fixed orthonormal vectors and external parameters. We derive variational formulas for the exponential asymptotics of the average number of total cr...

Vanessa Piccolo · 0 citations
Preprint Aug 2026

Spectral phase transitions in Gaussian multi-index models

It is proved that the AMP-derived preprocessing of [Defilippis et al., 2025] is optimal among all bounded matrix-valued preprocessing maps of any fixed dimension and the general spectral conjecture of [Defilippis et al., 2025] is proved.

Florent Krzakala, Pierre Mergny, Vanessa Piccolo · 0 citations

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