This paper establishes log-concavity of the ground state for a large family of discrete, 1-dimensional Schrödinger operators, extending the analysis of the Hamming weight with a spike problem to more…

This paper settles the complexity of three sketching problems in graphs and distributions.

This paper provides non-asymptotic and explicit estimates for the exponential deviation inequalities of the HyperLogLog estimator.

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

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 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 systematically explores the convex polygon reconstruction problem with specified sets of features, contributing new testing algorithms and hardness results.

The paper establishes information-theoretic lower bounds for stochastic optimization using low-bit gradients by reducing the problem to compressed Gaussian mean estimation, yielding sharp bounds on co…

This paper proves that a majority of filled-in Sudoku grids require a logarithmic fraction of cells to be filled by clues, and constructs grids requiring 18 and 80 clues for 9x9 and 16x16 Sudoku, resp…

The paper develops a unified theoretical framework to systematically characterize the optimal privacy-utility trade-off (PUT) and optimal Local Differential Privacy (LDP) channels for general statisti…

This paper proves conditions for efficiently approximating expectations of certain functions with respect to standard Gaussian or symmetric exponential probability measures.

The paper establishes conditions for QUBO formulations of combinatorial optimization problems that guarantee valid binary and feasible local minimizers using gradient-based methods.

This paper investigates how the extremality of fixed-volume spanning trees changes based on product-grid boundary factors in two and arbitrary dimensions.

This paper introduces Curvature-Weighted Gradient Diversity (CWGD), a geometry-aware measure for optimization noise that reduces the asymptotic optimization error floor by up to a factor of two compar…