Talagrand
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Layerwise Terminal Discrepancy in Chen's Reverse-Heat Coupling on the Boolean Cube
arXiv:2606.04573v1 Announce Type: cross Abstract: We isolate a layerwise refinement of the terminal testing-discrepancy step in Chen's perturbed reverse-heat approach~\cite{Chen2026} to Talagrand's convolution conjecture on the Boolean cube. Built on the joint-filtration martingale formulation of Chen's coupling, and on Chen's approximate monotonicity and conditional squared-score estimates being available in the joint-filtration form stated below, we prove the localized testing estimate \[...
Pointwise Complexity for Gaussian Fields: Upper Envelopes, Algorithmic Lower Bounds, and Separation
Announce Type: cross Abstract: We prove a variance-aware pointwise majorizing-measure theorem for centered Gaussian processes. Classical generic chaining characterizes the scalar quantity $\mathbb E\sup_{x\in T}X_x$; the theorem here gives a simultaneous high-probability envelope for the entire field. For an ambient prior $\mu$, the envelope at $x$ is governed by a pointwise Fernique-Talagrand functional...
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