On the expected number of real roots of random polynomials arising from evolutionary game theory

On the Number of Real Roots of Random Polynomials

Roots of random polynomials have been studied exclusively in both analysis and probability for a long time. A famous result by Ibragimov and Maslova, generalizing earlier fundamental works of Kac and Erdős-Offord, showed that the expectation of the number of real roots is 2 π logn + o(logn). In this paper, we determine the true nature of the error term by showing that the expectation equals 2 π...

the effect of traffic density on the accident externality from driving the case study of tehran

در این پژوهش به بررسی اثر افزایش ترافیک بر روی تعداد تصادفات پرداخته شده است. به این منظور 30 تقاطع در شهر تهران بطور تصادفی انتخاب گردید و تعداد تصادفات ماهیانه در این تقاطعات در طول سالهای 89-90 از سازمان کنترل ترافیک شهر تهران استخراج گردید و با استفاده از مدل داده های تابلویی و نرم افزار eviews مدل خطی و درجه دوم تخمین زده شد و در نهایت این نتیجه حاصل شد که تقاطعات پر ترافیک تر تعداد تصادفا...

On the Expected Number of Real Roots of a System of Random Polynomial Equations

We unify and generalize several known results about systems of random polynomials. We first classify all orthogonally invariant normal measures for spaces of polynomial mappings. For each such measure we calculate the expected number of real zeros. The results for invariant measures extend to underdetermined systems, giving the expected volume for orthogonally invariant random real projective v...

On the Number of Real Roots of Polynomials

Our main theorem, proved in § 2 establishes some of the properties of F(x, y) = 0 when we drop all restrictions on / and require only that all the roots of h be real (of arbitrary sign). In the last section, we apply this theorem to obtain an extension of Theorem 1.1 which states that, for h restricted as in Pόlya's theorem, there are at least as many intersection points as the number of real r...

Expected Number of Local Maxima of Some Gaussian Random Polnomials