Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501293 | Journal of Complexity | 2005 | 17 Pages |
Abstract
We consider a random polynomial system with m equations and m real unknowns. Assume all equations have the same degree d and the law on the coefficients satisfies the Kostlan-Shub-Smale hypotheses. It is known that E(NX)=dm/2 where NX denotes the number of roots of the system. Under the condition that d does not grow very fast, we prove that limsupmâ+âVarNXdm/2⩽1. Moreover, if d⩾3 then VarNXdm/2â0 as mâ+â, which implies NXdm/2â1 in probability.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mario Wschebor,