In 1943, Littlewood and Offord proved the first anti-concentration result for sums of independent random variables. Their result has since then been strengthened and generalized by generations of researchers, with applications in several areas of mathematics. In this paper, we present the first non-abelian analogue of the Littlewood–Offord result, a sharp anti-concentration inequality for products of independent random variables.
- Anti-concentration inequalities
- Littlewood–Offord–Erdős theorem
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