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math.PR2026
On Feige's conjecture
Zipei Nie, Jiaye Wei
We present a short proof of Feige's conjecture: for independent nonnegative random variables with expectation one, the probability that their sum is less than is at least…
math.PR2022★ 2 cited
The number of correct guesses with partial feedback
Zipei Nie
We consider the following game. A deck with copies of each of distinct cards is shuffled in a perfectly random way. The Guesser sequentially guesses the card from top to bo…
math.PR2021★ 2 cited
Matrix anti-concentration inequalities with applications
Zipei Nie
We provide a polynomial lower bound on the minimum singular value of an random matrix with jointly Gaussian entries, under a polynomial bound on the matrix norm and…