Asymptotic results for random polynomials on the unit circle

• Autorzy: Tucci G. H. , Whiting P.
• Języki publikacji: EN

Abstrakty

EN

In this paper we study the asymptotic behavior of the maximum magnitude of a complex random polynomial with i.i.d. uniformly distributed random roots on the unit circle. More specifically, let {n_k}^∞_k=1 be an infinite sequence of positive integers and let {z_k}^∞_k=1 be a sequence of i.i.d. uniformly distributed random variables on the unit circle. The above pair of sequences determine a sequence of random polynomials P_N(z) = Π^N_k=1 (z − z_k)^nk with random roots on the unit circle and their corresponding multiplicities. In this work, we show that subject to a certain regularity condition on the sequence {n_k}^∞_k=1, the log maximum magnitude of these polynomials scales as _sNI*, where s²_N = Σ^N_k=1 n²_k and I* is a strictly positive random variable.

Słowa kluczowe

EN

random polynomials; brownian bridge; stochastic process

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2014
• Tom: Vol. 34, Fasc. 2
• Strony: 181--197
• Opis fizyczny: Bibliogr. 16 poz., wykr.

Twórcy

autor

Tucci G. H.

• Barclays Capital Inc., 745th Seventh Avenue, New York, 10007, USA

autor

Whiting P.

• Macquarie University, Dept. Engineering, Level 2, Building E6A, North Ryde, NSW 0209, Australia

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).