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On the Number of Real Zeros of Random Fewnomials
Citation key BET-On-the-Number-of-Real-Zeros-of-Random-Fewnomials
Author Peter Bürgisser and Alperen A. Ergür and Josué Tonelli-Cueto
Pages 721–732
Year 2019
DOI 10.1137/18M1228682
Journal SIAM Journal on Applied Algebra and Geometry
Volume 3
Number 4
Abstract Consider a system $f_1(x)=0,łdots,f_n(x)=0$ of $n$ random real polynomial equations in $n$ variables, where each $f_i$ has a prescribed set of exponent vectors described by a set $A\subseteq \mathbbN^n$ 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 $\frac12^n-1\binomtn$.
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