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Random polynomials

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Published by Academic Press in Orlando, Fla .
Written in English


  • Random polynomials

Book details:

Edition Notes

Includes bibliographies and index.

StatementA.T. Bharucha-Reid, M. Sambandham.
SeriesProbability and mathematical statistics
ContributionsSambandham, M.
LC ClassificationsQA273.43 .B48 1986
The Physical Object
Paginationxv, 206 p. :
Number of Pages206
ID Numbers
Open LibraryOL2538986M
ISBN 100120957108, 0120957116
LC Control Number85019961

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The book takes a look at convergence and limit theorems for random polynomials and distribution of the zeros of random algebraic polynomials, including limit theorems for random algebraic polynomials and random companion matrices and distribution of the zeros of random algebraic polynomials.   Random Polynomials: Probability and Mathematical Statistics: A Series of Monographs and Textbooks - Kindle edition by A. T. Bharucha-Reid, M. Sambandham, Z. W. Brinbaum, E. Lukacs. Download it once and read it on your Kindle device, PC, phones or tablets. ISBN: OCLC Number: Description: xv, pages: illustrations ; 24 cm. Contents: Introduction --Random algebraic polynomials: basic definitions and properties --Random matrices and random algebraic polynomials --The number and expected number of real zeros of random algebraic polynomials --The number and . to factor random polynomials of very large degree (, and more) over F 2 in less than a day; see also [18] for more related results. The Shape of a Random Polynomial over a Finite Field. As we com-mented in the previous section, bivariate generating functions are typical tools in ana-.

Topics in Random Polynomials presents a rigorous and comprehensive treatment of the mathematical behavior of different types of random polynomials. These polynomials-the subject of extensive recent research-have many applications in physics, economics, and statistics. The main results are presented in such a fashion that they can be understood and used by readers whose knowledge of probability.   Abstract. In this paper, we survey old and new results about random univariate polynomials over a finite field \(\mathbb{F}_q\).We are interested in three aspects: (1) the decomposition of a random polynomial in terms of its irreducible factors, (2) the usage of random polynomials in algorithms, and (3) the average-case analysis of algorithms that use polynomials over finite fields. There is Polynomials by u contains all the basics, and has a lot of exercises too. On a similar spirit is Polynomials by V.V. Prasolov. I've found the treatment in both these books very nice, with lots of examples/applications and history of the results.   We consider random polynomials with independent identically distributed coefficients with a fixed law. Assuming the Riemann hypothesis for Dedekind zeta functions, we prove that such polynomials are irreducible and their Galois groups contain the alternating group with high probability as the degree goes to infinity. This settles a conjecture of Odlyzko and Poonen conditionally on RH for.

Genre/Form: Electronic books: Additional Physical Format: Print version: Bharucha-Reid, A.T., (Albert T.). Random polynomials. Orlando, Florida ; London, England. Hence random polynomials are basic functions with which we construct very general random processes. There is also a relationship between solutions of random difference equations and random polynomials. Consider a stochastic difference equation () Xt = AtXt−1 +Bt, where {At,Bt} is a sequence of random variables. We will call () a. tic polynomials form a special class of random polynomials. See [15], or for a rst insight the Random matrix entry in Wikipedia. Random polynomials is a classical eld of interest in Mathematics and Statistics; several families o f random polynomials have been described in great detail, see [9]. The number and distribution of real and complex roots. Abstract. In the study of algebraic and numerical properties of polynomials one occasionally introduces the notion of a random polynomial. For example, this chapter was originally motivated by investigations, including [Ki, Re, SS, Sml, Sm2], into the complexity of root-finding algorithms for polynomials.