Approximate stochastic localization plus conductance transfers yield a weak Poincaré inequality for the SK model at β < 1/2, enabling efficient Glauber sampling from a warm start.
arXiv preprint arXiv:2504.20539 , year=
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
$\texttt{Randomstrasse101}$ is a blog dedicated to Open Problems in Mathematics, with a focus on Probability Theory, Computation, Combinatorics, Statistics, and related topics. This manuscript serves as a stable record of the Open Problems posted in 2024, with the goal of easing academic referencing. The blog can currently be accessed at $\texttt{randomstrasse101.math.ethz.ch}$.
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2026 4representative citing papers
Proves the Matrix Spencer conjecture for the left regular representation of every finite group by combining Peter-Weyl decomposition with intrinsic-freeness inequalities in an iterated partial-coloring argument.
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.
A model-independent framework converts mild low-degree testing advantages into conditional computational lower bounds for recovery tasks, recovering prior results for planted submatrix and SBM while providing new evidence for detection-recovery gaps in angular synchronization and multi-layer models.
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Weak Poincar\'e Inequalities via Approximate Stochastic Localization: Application to Sampling the Sherrington-Kirkpatrick Model
Approximate stochastic localization plus conductance transfers yield a weak Poincaré inequality for the SK model at β < 1/2, enabling efficient Glauber sampling from a warm start.
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Matrix Discrepancy for Representations of Finite Groups
Proves the Matrix Spencer conjecture for the left regular representation of every finite group by combining Peter-Weyl decomposition with intrinsic-freeness inequalities in an iterated partial-coloring argument.
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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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Algorithmic Contiguity from Low-Degree Heuristic II: Predicting Detection-Recovery Gaps
A model-independent framework converts mild low-degree testing advantages into conditional computational lower bounds for recovery tasks, recovering prior results for planted submatrix and SBM while providing new evidence for detection-recovery gaps in angular synchronization and multi-layer models.