This thesis is concerned with the characteristics and behaviours of random polynomi- als of a high degree. Random polynomials are polynomials with random coefficients and take the form '£']=0 ajxj, where the coefficients aj, (j = 0, ... , n) are random variables of a probability distribution, such as the normal or uniform distribution. The polynomials featured in this thesis are of the algebraic, hyperbolic and trigonometric type, all of which have coefficients that are independent random variables of the nor- mal distribution. In Chapter 1, we discuss the characteristics featured throughout this thesis, namely, the expected number of level crossings, the expected number of maxima( minima), the expected number of maxima below a fixed level u, the expected number of points of inflection as well as the covariance of the number of zeros. In this chapter we also present the formulae used in this thesis to prove the results obtained. In Chapter 2 we discuss results previously obtained for polynomials with similar characteristics to those featured in this thesis.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:550966 |
| Date | January 2011 |
| Creators | McGuinness, Bronagh |
| Publisher | University of Ulster |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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