The GHOST framework gives near-optimal conditions for universal Gaussian CLTs on linear spectral statistics of sample covariance matrices, with explicit mean-covariance corrections from a bilinear fourth-order kernel and applications to corrected sphericity tests.
A Variational Represen tation for Certain Function- als of Brownian Motion
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Introduces a TAP-motivated framework and constructs explicit parameter-free spectral algorithms that achieve strong detection and weak recovery thresholds in three canonical correlated two-view models with matching lower bounds.
Constructs weak solutions, proves anisotropic Besov regularity, and establishes uniqueness in the mass-preserving renormalized class for kinetic FP equations with nonlinear diffusion under mass-critical growth on Ψ.
Proves LDP for stationary solutions of SFDEs with infinite delay and extends to invariant measures via contraction principle.
Lecture notes providing an introduction to Wiener chaos decomposition, Gaussian fields on the torus, and applications to the Φ^4 model.
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The Geometry of Spectral Fluctuations: On Near-Optimal Conditions for Universal Gaussian CLTs, with Statistical Applications
The GHOST framework gives near-optimal conditions for universal Gaussian CLTs on linear spectral statistics of sample covariance matrices, with explicit mean-covariance corrections from a bilinear fourth-order kernel and applications to corrected sphericity tests.
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Optimal Spectral Algorithms for Correlated Two-view Models in High Dimensions
Introduces a TAP-motivated framework and constructs explicit parameter-free spectral algorithms that achieve strong detection and weak recovery thresholds in three canonical correlated two-view models with matching lower bounds.
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Kinetic Fokker-Planck Equations with Nonlinear Diffusion
Constructs weak solutions, proves anisotropic Besov regularity, and establishes uniqueness in the mass-preserving renormalized class for kinetic FP equations with nonlinear diffusion under mass-critical growth on Ψ.
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Large deviation principle for the stationary solutions of stochastic functional differential equations with infinite delay
Proves LDP for stationary solutions of SFDEs with infinite delay and extends to invariant measures via contraction principle.
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Topics in Gaussian Wiener chaos expansion
Lecture notes providing an introduction to Wiener chaos decomposition, Gaussian fields on the torus, and applications to the Φ^4 model.
- Explicit cutoff profiles for colored top-$m$-to-random shuffles