%0 Journal Article %1 burgisser2018number %A Bürgisser, Peter %A Ergür, Alperen A. %A Tonelli-Cueto, Josué %D 2018 %K fewnomials random %T On the Number of Real Zeros of Random Fewnomials %U http://arxiv.org/abs/1811.09425 %X Consider a system $f_1(x)=0,łdots,f_n(x)=0$ of $n$ random real polynomials in $n$ variables, where each $f_i$ has a prescribed set of terms described by a set $AN^n$ of cardinality $t$. Assuming that the coefficients of the $f_i$ are independent Gaussians of any variance, we prove that the expected number of zeros of the random system in the positive orthant is bounded from above by $2tn$.

@article{burgisser2018number, abstract = {Consider a system $f_1(x)=0,\ldots,f_n(x)=0$ of $n$ random real polynomials in $n$ variables, where each $f_i$ has a prescribed set of terms described by a set $A\subseteq \mathbb{N}^n$ of cardinality $t$. Assuming that the coefficients of the $f_i$ are independent Gaussians of any variance, we prove that the expected number of zeros of the random system in the positive orthant is bounded from above by $2\binom{t}{n}$.}, added-at = {2019-07-28T16:05:01.000+0200}, author = {Bürgisser, Peter and Ergür, Alperen A. and Tonelli-Cueto, Josué}, biburl = {https://www.bibsonomy.org/bibtex/274f9efe5e9c8b40b236ed7bbf31e5357/gjindal}, description = {On the Number of Real Zeros of Random Fewnomials}, interhash = {be753b022d737b7e5600ec0d88678d84}, intrahash = {74f9efe5e9c8b40b236ed7bbf31e5357}, keywords = {fewnomials random}, note = {cite arxiv:1811.09425Comment: 10 pages. Fixed an error in the proof of Corollary 2.2, which led to changes in some of the constants. Added a missing reference. Added proof of better bound for the univariate case}, timestamp = {2019-07-28T16:05:01.000+0200}, title = {On the Number of Real Zeros of Random Fewnomials}, url = {http://arxiv.org/abs/1811.09425}, year = 2018 }