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Motivated by the recent paper of Hollom and Portier (arXiv: 2306.07811v1), we study the anti-concentration function $(0, \\infty)\\ni y\\to \\inf_{\\alpha}\\mathbf{P}\\left(|X_{\\alpha}-\\mathbf{E}[X_{\\alpha}]|\\geq y \\sqrt{{\\rm Var}(X_{\\alpha})}\\right)$ and find its explicit expression. 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