The number of real roots for random trigonometric polynomials: universality and non-universality of the variance
Báo cáo viên: Assoc. Prof. Đỗ Quang Yên ( University of Virginia, USA)

Thời gian: 14h Thứ 5, ngày 17/06/2021

Địa điểm: 301 nhà A5 hoặc online qua link


Tóm tắt: We study the number of real roots of random trigonometric polynomials with iid coefficients of mean zero and bounded moments. We show that the variance of this number is asymptotically linear in terms of the expectation. This result extends a prior work of Bally, Caramellino, and Poly (where some smoothness conditions are required for the coefficient distributions). In particular, our methods work for discrete trigonometric polynomials. Joint work with Hoi Nguyen (Ohio State) and Oanh Nguyen (UIUC).

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