ESTIMATES FOR THE CONCENTRATION FUNCTIONS IN THE LITTLEWOOD-OFFORD PROBLEM

摘要

Let X, X_1,..., X_n be independent, identically distributed random, variables. In this paper, we study the behavior of concentration functions of the weighted sums n∑k=1 a_kX_k with respect to the arithmetic structure of coefficients a_k. Such concentration results recently became important in connection with the study of singular values of random matrices. In this paper, we formulate and prove some refinements of a result of Vershynin (2014). Bibliography: 28 titles.