報告人：高云石 博士

報告題目：Large deviations and central limit theorem for weakly interacting diffusions in Erd?s-Rényi graph

報告時間：2025年11月8日（周六）上午9：00

報告地點：云龍校區(qū)6號樓304會議室

主辦單位：數(shù)學(xué)與統(tǒng)計學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報告人簡介：

高云石，安徽師范大學(xué)講師，研究方向為隨機(jī)過程及其應(yīng)用，目前的研究主要集中在弱交互粒子系統(tǒng)領(lǐng)域，論文發(fā)表在SPA，JTP，SPL等概率論期刊，主持國家自然科學(xué)基金青年項目1項。

報告摘要：

In this talk, we study a particle systems (or interacting diffusions) on an Erd?s-Rényi graph with the parameter p_N in (0,1] . Our aim is to establish the large deviations and central limit theorem for the empirical measure process of particle systems under the condition Np_N^4→∞and Np_N^{3+ε}→∞ as N→∞, respectively, where N is the number of particles. Use exponential equivalence and multilinear extensions of Grothendieck inequality to prove the large deviations. For central limit theorem, its proof mainly relies on the estimation of the operator of diffusion processes in the Sobolev space.