Any centered 1-subgaussian random vector equals the sum of a universal number of standard Gaussians, solving Talagrand's convexity conjecture.
arXiv preprint arXiv:2507.00346 , year =
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Empirical spectral distributions of arbitrary-degree polynomials in Ginibre matrices converge to their Brown measures as matrix size tends to infinity.
Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.
Asymptotic expansions in 1/N² are established for traces and transport maps in multimatrix models with convex potentials, implying strong convergence.
Proposes a random matrix analogue of the Akemann-Ostrand property for free groups and that random embeddings of L(F_2) into matrix ultraproducts are existential.
citing papers explorer
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On Talagrand's Convexity Conjecture
Any centered 1-subgaussian random vector equals the sum of a universal number of standard Gaussians, solving Talagrand's convexity conjecture.
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Brown measure convergence for the spectrum of polynomials in Ginibre matrices
Empirical spectral distributions of arbitrary-degree polynomials in Ginibre matrices converge to their Brown measures as matrix size tends to infinity.
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Potential Hessian Ascent III: Sampling the Sherrington--Kirkpatrick Model at Beta < 1/2
Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.
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Asymptotic expansion for transport maps between laws of multimatrix models
Asymptotic expansions in 1/N² are established for traces and transport maps in multimatrix models with convex potentials, implying strong convergence.
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Questions on the structure of random embeddings of $L(\mathbb{F}_2)$
Proposes a random matrix analogue of the Akemann-Ostrand property for free groups and that random embeddings of L(F_2) into matrix ultraproducts are existential.