ON THE DISTRIBUTION OF COMPLEX ROOTS OF RANDOM POLYNOMIALS WITH HEAVY-TAILED COEFFICIENTS

Götze F, Zaporozhets D (2012)
Theory Of Probability & Its Applications 56(4): 696-U217.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
Consider a random polynomial G(n)(z) = xi(n)z(n) + . . . + xi(1)z + xi(0) with independent identically distributed complex-valued coefficients. Suppose that the distribution of log(1 + log(1 + vertical bar xi(0)vertical bar)) has a slowly varying tail. Then the distribution of the complex roots of G(n) concentrates in probability, as n -> infinity, to two centered circles and is uniform in the argument as n -> infinity. The radii of the circles are vertical bar xi(0)/xi(tau)vertical bar(1/tau) and vertical bar xi(tau)/xi(n)vertical bar(1/(n-tau)), where xi(tau) denotes the coefficient with the maximum modulus.
Erscheinungsjahr
Zeitschriftentitel
Theory Of Probability & Its Applications
Band
56
Ausgabe
4
Seite(n)
696-U217
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Götze F, Zaporozhets D. ON THE DISTRIBUTION OF COMPLEX ROOTS OF RANDOM POLYNOMIALS WITH HEAVY-TAILED COEFFICIENTS. Theory Of Probability & Its Applications. 2012;56(4):696-U217.
Götze, F., & Zaporozhets, D. (2012). ON THE DISTRIBUTION OF COMPLEX ROOTS OF RANDOM POLYNOMIALS WITH HEAVY-TAILED COEFFICIENTS. Theory Of Probability & Its Applications, 56(4), 696-U217. doi:10.1137/S0040585X9798573X
Götze, F., and Zaporozhets, D. (2012). ON THE DISTRIBUTION OF COMPLEX ROOTS OF RANDOM POLYNOMIALS WITH HEAVY-TAILED COEFFICIENTS. Theory Of Probability & Its Applications 56, 696-U217.
Götze, F., & Zaporozhets, D., 2012. ON THE DISTRIBUTION OF COMPLEX ROOTS OF RANDOM POLYNOMIALS WITH HEAVY-TAILED COEFFICIENTS. Theory Of Probability & Its Applications, 56(4), p 696-U217.
F. Götze and D. Zaporozhets, “ON THE DISTRIBUTION OF COMPLEX ROOTS OF RANDOM POLYNOMIALS WITH HEAVY-TAILED COEFFICIENTS”, Theory Of Probability & Its Applications, vol. 56, 2012, pp. 696-U217.
Götze, F., Zaporozhets, D.: ON THE DISTRIBUTION OF COMPLEX ROOTS OF RANDOM POLYNOMIALS WITH HEAVY-TAILED COEFFICIENTS. Theory Of Probability & Its Applications. 56, 696-U217 (2012).
Götze, Friedrich, and Zaporozhets, D. “ON THE DISTRIBUTION OF COMPLEX ROOTS OF RANDOM POLYNOMIALS WITH HEAVY-TAILED COEFFICIENTS”. Theory Of Probability & Its Applications 56.4 (2012): 696-U217.