Mean number of real zeros of a random hyperbolic polynomial
Consider the random hyperbolic polynomial, f(x)=1pa1coshx+⋯+np×ancoshnx, in which n and p are integers such that n≥2, p≥0, and the coefficients ak(k=1,2,…,n) are independent, standard normally distributed random variables. If νnp is the mean number of real zeros of f(x), then we prove that νnp=π−1...
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171200001848 |
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| _version_ | 1832559040103710720 |
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| author | J. Ernest Wilkins |
| author_facet | J. Ernest Wilkins |
| author_sort | J. Ernest Wilkins |
| collection | DOAJ |
| description | Consider the random hyperbolic polynomial, f(x)=1pa1coshx+⋯+np×ancoshnx, in which n and p are integers such that n≥2, p≥0, and the coefficients ak(k=1,2,…,n) are independent, standard normally
distributed random variables. If νnp is the mean number of real zeros of f(x), then we prove that νnp=π−1 logn+O{(logn)1/2}. |
| format | Article |
| id | doaj-art-ebcd45f50c024e2cafb7fcee92f32a42 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ebcd45f50c024e2cafb7fcee92f32a422025-02-03T01:30:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0123533534210.1155/S0161171200001848Mean number of real zeros of a random hyperbolic polynomialJ. Ernest Wilkins0Department of Mathematics, Clark Atlanta University, Atlanta 30314, GA, USAConsider the random hyperbolic polynomial, f(x)=1pa1coshx+⋯+np×ancoshnx, in which n and p are integers such that n≥2, p≥0, and the coefficients ak(k=1,2,…,n) are independent, standard normally distributed random variables. If νnp is the mean number of real zeros of f(x), then we prove that νnp=π−1 logn+O{(logn)1/2}.http://dx.doi.org/10.1155/S0161171200001848Random polynomialsreal zeroshyperbolic polynomials Kac-Rice formula. |
| spellingShingle | J. Ernest Wilkins Mean number of real zeros of a random hyperbolic polynomial International Journal of Mathematics and Mathematical Sciences Random polynomials real zeros hyperbolic polynomials Kac-Rice formula. |
| title | Mean number of real zeros of a random hyperbolic polynomial |
| title_full | Mean number of real zeros of a random hyperbolic polynomial |
| title_fullStr | Mean number of real zeros of a random hyperbolic polynomial |
| title_full_unstemmed | Mean number of real zeros of a random hyperbolic polynomial |
| title_short | Mean number of real zeros of a random hyperbolic polynomial |
| title_sort | mean number of real zeros of a random hyperbolic polynomial |
| topic | Random polynomials real zeros hyperbolic polynomials Kac-Rice formula. |
| url | http://dx.doi.org/10.1155/S0161171200001848 |
| work_keys_str_mv | AT jernestwilkins meannumberofrealzerosofarandomhyperbolicpolynomial |