For maxima of identically distributed random variables, the paper gives sharp anti-concentration bounds under arbitrary dependence, and sharper bounds under a new convexity condition on the copula's diagonal.
D., Feng, Y., and Underwood, W
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Sharp Anti-Concentration Inequalities for Extremum Statistics via Copulas
For maxima of identically distributed random variables, the paper gives sharp anti-concentration bounds under arbitrary dependence, and sharper bounds under a new convexity condition on the copula's diagonal.