scholarly journals Correlations between zeros of a random polynomial

1997 ◽  
Vol 88 (1-2) ◽  
pp. 269-305 ◽  
Author(s):  
Pavel Bleher ◽  
Xiaojun Di
Keyword(s):  
Random Polynomial ◽  
Correlations Between Zeros

scholarly journals Universality and scaling of correlations between zeros on complex manifolds

2000 ◽  
Vol 142 (2) ◽  
pp. 351-395 ◽  
Author(s):  
Pavel Bleher ◽  
Bernard Shiffman ◽  
Steve Zelditch
Keyword(s):  
Complex Manifolds ◽  
Correlations Between Zeros

scholarly journals Asymptotic variance of the number of real roots of random polynomial systems

2018 ◽  
Vol 146 (12) ◽  
pp. 5437-5449 ◽  
Author(s):  
D. Armentano ◽  
J-M. Azaïs ◽  
F. Dalmao ◽  
J. R. León
Keyword(s):  
Asymptotic Variance ◽  
Polynomial Systems ◽  
Random Polynomial ◽  
Real Roots ◽  
Number Of Real Roots

scholarly journals Joint distribution of conjugate algebraic numbers: A random polynomial approach

2020 ◽  
Vol 359 ◽  
pp. 106849 ◽  
Author(s):  
Friedrich Götze ◽  
Denis Koleda ◽  
Dmitry Zaporozhets
Keyword(s):  
Joint Distribution ◽  
Random Polynomial ◽  
Algebraic Numbers ◽  
Conjugate Algebraic Numbers

Finding a Longest Alternating Cycle in a 2-edge-coloured Complete Graph is in RP

1996 ◽  
Vol 5 (3) ◽  
pp. 297-306 ◽  
Author(s):  
Rachid Saad
Keyword(s):  
Complete Graph ◽  
Strong Evidence ◽  
General Setting ◽  
Maximum Length ◽  
Sufficient Condition ◽  
Complete Graphs ◽  
Random Polynomial ◽  
Exact Matching ◽  
Matching Problem ◽  
Bipartite Tournament

Jackson [10] gave a polynomial sufficient condition for a bipartite tournament to contain a cycle of a given length. The question arises as to whether deciding on the maximum length of a cycle in a bipartite tournament is polynomial. The problem was considered by Manoussakis [12] in the slightly more general setting of 2-edge coloured complete graphs: is it polynomial to find a longest alternating cycle in such coloured graphs? In this paper, strong evidence is given that such an algorithm exists. In fact, using a reduction to the well known exact matching problem, we prove that the problem is random polynomial.

scholarly journals Level crossings and turning points of random hyperbolic polynomials

1999 ◽  
Vol 22 (3) ◽  
pp. 579-586
Author(s):  
K. Farahmand ◽  
P. Hannigan
Keyword(s):  
Asymptotic Estimate ◽  
Turning Points ◽  
Random Variables ◽  
Random Polynomial ◽  
Expected Number ◽  
Hyperbolic Polynomial ◽  
Level Crossings ◽  
Hyperbolic Polynomials ◽  
Normally Distributed

In this paper, we show that the asymptotic estimate for the expected number ofK-level crossings of a random hyperbolic polynomiala1sinhx+a2sinh2x+⋯+ansinhnx, whereaj(j=1,2,…,n)are independent normally distributed random variables with mean zero and variance one, is(1/π)logn. This result is true for allKindependent ofx, providedK≡Kn=O(n). It is also shown that the asymptotic estimate of the expected number of turning points for the random polynomiala1coshx+a2cosh2x+⋯+ancoshnx, withaj(j=1,2,…,n)as before, is also(1/π)logn.

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