Inequalities and tail bounds for elementary symmetric polynomial with applications
نویسندگان
چکیده
This paper studies the elementary symmetric polynomials Sk(x) for x ∈ Rn. We show that if |Sk(x)|, |Sk+1(x)| are small for some k > 0 then |Sl(x)| is also small for all l > k. We use this to prove probability tail bounds for the symmetric polynomials when the inputs are only t-wise independent, that may be useful in the context of derandomization. We also provide examples of t-wise independent distributions for which our bounds are essentially tight.
منابع مشابه
Inequalities and tail bounds for elementary symmetric polynomial
This paper studies the elementary symmetric polynomials Sk(x) for x ∈ Rn. We show that if |Sk(x)|, |Sk+1(x)| are small for some k > 0 then |S`(x)| is also small for all ` > k. We use this to prove probability tail bounds for the symmetric polynomials when the inputs are only t-wise independent, which may be useful in the context of derandomization. We also provide examples of t-wise independent...
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