The paper proves an information-theoretically optimal gap-majority lemma in the two-player randomized communication model, achieving the correct linear scaling and constant-constant tradeoff.

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 provides bounds on the difference between the annihilation number and independence number of a finite simple graph, and proves these bounds for various types of graphs.

The paper refutes Steurer's conjecture regarding the existence of large constant-separated sets within families of unit-norm vectors with low average correlation, using high-dimensional expanders to s…

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

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.

The paper establishes new hardness amplification results for Learning Parity with Noise (LPN) and its sparse variants, showing that solving the problem on a small fraction of instances implies solving…

This paper establishes an unconditional barrier for AC0-natural proofs, showing that they cannot prove lower bounds greater than $2^{n^{7/(d-5)}}$ against depth-$d$ circuits.

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…

The paper introduces novel, efficient differentially private algorithms for estimating monotone statistics, significantly improving sample complexity compared to existing methods.

The paper proposes using an LLM aggregator that analyzes complete reasoning traces, demonstrating that trace-level synthesis is superior to traditional consensus methods like majority voting for solvi…

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 shows that finite unions of intersecting affine modules in one dimension are efficiently exactly learnable using equivalence and subset queries.

This paper introduces a new distributed computational model called the uniform port model, which allows for efficient self-stabilizing algorithms for local symmetry breaking problems on general graphs…

This paper improves an algorithm for computing lower bounds on the margin of a Single Transferable Vote (STV) election, making risk-limiting audits more practical.