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Anti-concentration bounds for folded normal and inverse of gaussian variables

Are there any easy to use bounds on sums of the following kind : $$ \sum_{i = 1}^{i = N} |a_i| \geq P \\ a_i \sim \mathcal{N}(0, 1) \\ $$ and also for sums of the form : $$ \sum_{i = 1}^{i = M} \...
Govind Gopakumar's user avatar