報告人簡介
魯大偉，大連理工大學教授，博士生導師。2004年畢業于大連理工大學，獲學士學位；2009年畢業于大連理工大學，獲博士學位。主要研究方向：極限理論、精細大偏差、破產概率、概率不等式等。在國內外學術刊物Insurance: Mathematics and Economics，Journal of Theoretical Probability, Statistics & Probability Letter, Methodology and Computing in Applied Probability等傳統概率雜志以及Proceedings of the American Mathematical Society，CSIAM Transactions on Applied Mathematics等綜合性雜志上發表學術論文數十篇。負責主持國家自然科學基金，青年項目一項，面上項目兩項。承擔校企合作產學研橫向課題十多項。目前分別擔任中國現場統計研究會教育統計與管理分會, 統計交叉科學研究分會理事。
內容簡介
Motivated by the questions posed by W. V. Li and A. Wei and the conjecture of E. Lundberg and A. Thomack, we study the expected number of zeros of random harmonic polynomials with independently and identically distributed Gaussian coefficients. We verify the conjecture of E. Lundberg and A. Thomack that the expectation is O(n) when deg p = α deg q, where 0 < α < 1. This result extends the previous estimates when m is a fixed constant or m = n to more general case.
