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The random sum\n  $$S_A := a_1 \\xi_1 + ... + a_n \\xi_n $$\nwhere $\\xi_i$ are iid copies of $\\xi$ is of fundamental importance in probability and its applications.\n  We discuss the small ball problem, the aim of which is to estimate the maximum probability that $S_A$ belongs to a ball with given small radius, following the discovery made by Littlewood-Offord and Erdos almost 70 years ago. 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