The paper proves a stochastic comparison for Gaussian maxima, resolving the Weak Simplex Conjecture and proving the Simplex Mean Width Conjecture.

This paper introduces a structural theorem for the sparsifiability of real-valued codes, which generalizes both combinatorial and continuous notions of sparsification.

This paper proves that random linear codes have nearly optimal discrepancy properties in various regimes, extending classical results and enabling new applications.

This paper introduces and studies the block tensor rank of sum-rank metric codes, showing its additive decomposition and deriving lower bounds.

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…

This paper establishes recovery guarantees for low-rank Hermitian matrices from quadratic sampling matrices under the assumption of finite 4+δ moments of the entries.

A new boosting algorithm that strong learns concept classes closed under O(log 1/γ)-XOR using O(log 1/ε) calls to a γ-advantage weak learner and additional samples, by connecting boosting with list-de…

This paper proves an inverse-polynomial spectral-gap bound for the lazy swap chain on binary matrices with prescribed row and column sums, which is a standard sampler for fixed-margin null models.

This paper presents a local computation algorithm to approximate the top eigenvector of a symmetric matrix with entries between -1 and 1, building on Swartworth and Woodruff's work.

This paper shows that sub-dictionaries sampled from a coherent dictionary using a coherence rejective Poisson sampling model are well-conditioned with high probability, as long as their expected size…

The polynomial-time low-degree conjecture, which predicts that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling imply polynomial-time ha…

This paper proves that for any finite abelian group, there exists a spectral sparsifier for its Cayley graph with log(|G|) generators. This result improves upon previous work for constructing code spa…

This paper derives bounds on the probability of incorrect clustering of noisy short sequences using statistically optimal rules, focusing on DNA storage decoders.

This paper shows that any boolean matrix with bounded factorization norm can be expressed as a signed sum of blow-up identity matrices, and this result has applications to matrix sequences and complex…