2016/12/29 by Manjunath Krishnapur, Sourav Sarkar, Krishnapur, Manjunath +1
Mathematics · #60E15 #60G50 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1612.09045
openalex publication_date 2016/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given two vectors in Euclidean space, how unlikely is it that a random vector has a larger inner product with the shorter vector than with the longer one? When the random vector has independent, identically distributed components, we conjecture that this probability is no more than a constant multiple of the ratio of the Euclidean norms of the two given vectors, up to an additive term to allow for the possibility that the longer vector has more arithmetic structure. We give some partial results to support the basic conjecture.