@article{BB-The-Real-Tau-Conjecture-Is-True-On-Average,
Title = {The real tau-conjecture is true on average},
Author = {Ir\´en\´e Briquel and Peter Bürgisser},
Year = {2020},
Doi = {10.1002/rsa.20926},
Journal = {Random Structures & Algortihms},
Note = {This is an online version before inclusion in an issue of the journal.},
Abstract = {Koiran's real $\tau$-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 $O(mk^2t)$.},
Url = {http://arxiv.org/abs/1806.00417},
Url2 = {https://onlinelibrary.wiley.com/doi/full/10.1002/rsa.20926}
}