Geodesic
Expected number of real zeros of a random polynomial with independent identically distributed symmetric long-tailed coefficients
Teoriâ veroâtnostej i ee primeneniâ, Tome 55 (2010) no. 1, pp. 196-204 
L. Shepp; K. Farahmand. Expected number of real zeros of a random polynomial with independent identically distributed symmetric long-tailed coefficients. Teoriâ veroâtnostej i ee primeneniâ, Tome 55 (2010) no. 1, pp. 196-204. http://geodesic.mathdoc.fr/item/TVP_2010_55_1_a14/
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[1] Bharucha-Reid A. T., Sambandham M., Random Polynomials, Academic Press, Orlando, 1986, 206 pp. | MR | Zbl

[2] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1984, 752 pp. | MR

[3] Khardi G. G., Littlvud Dzh. E., Polia G., Neravenstva, IL, M., 1948, 456 pp.

[4] Kac M., “On the average number of real roots of a random algebraic equation”, Bull. Amer. Math. Soc., 49 (1943), 314–320 | DOI | MR | Zbl

[5] Kats M., Veroyatnost i smezhnye voprosy v fizike, Mir, M., 1965, 407 pp. | Zbl

[6] Kac M., Enigmas of Chance: An Autobiography, Harper Row, New York, 1985, 163 pp. | MR | Zbl

[7] Kac M., “On the average number of real roots of a random algebraic equation. II”, Proc. London Math. Soc., 50 (1949), 390–408 | DOI | MR

[8] Rice S. O., “Mathematical analysis of random noise”, System Tech. J., 25 (1945), 46–156 | MR

[9] Logan B. F., Shepp L. A., “Real zeros of random polynomials”, Proc. London Math. Soc., 18 (1968), 29–35 | DOI | MR | Zbl

[10] Logan B. F., Shepp L. A., “Real zeros of random polynomials. II”, Proc. London Math. Soc., 18 (1968), 308–314 | DOI | MR | Zbl

[11] Ibragimov I. A., Maslova N. B., “Srednee chislo nulei sluchainykh polinomov”, Vestn. Leningr. un-ta, 23:19 (1968), 171–172 | MR | Zbl

[12] Zaporozhets D. N., “Primer sluchainogo polinoma s neobychnym povedeniem kornei”, Teoriya veroyatn. i ee primen., 50:3 (2005), 549–555 | MR

[13] Ibragimov I. A., Zaporozhets D., On the distribution of roots of random polynomials, Preprint NoA306-060, Bielefeld University, 2006

[14] Dembo A., Poonen B., Shao Q., Zeitouni O., “Random polynomials having few or no zeros”, J. Amer. Math. Soc., 15:4 (2002), 857–892 | DOI | MR | Zbl

[15] Zaporozhets D. N., Nazarov A. I., “Kak malo byvaet kornei u sluchainogo polinoma v srednem”, Teoriya veroyatn. i ee primen., 53:1 (2008), 40–58 | MR