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| Zitatschlüssel | BB-The-Real-Tau-Conjecture-Is-True-On-Average |
|---|---|
| Autor | Iréné Briquel and Peter Bürgisser |
| Jahr | 2018 |
| Monat | 06 |
| Zusammenfassung | Koiran's real τ-conjecture claims that the number of real zeros of a structured polynomial given as a sum of $m$ products of $k$ real sparse polynomials, each with at most $t$ monomials, is bounded by a polynomial in $m,k,t$. This conjecture has a major consequence in complexity theory since it would lead to superpolynomial bounds for the arithmetic circuit size of the permanent. We confirm the conjecture in a probabilistic sense by proving that if the coefficients involved in the description of $f$ are independent standard Gaussian random variables, then the expected number of real zeros of $f$ is $O(mkt)$, which is linear in the number of parameters. |
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