報(bào)告人：高云石 博士

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

報(bào)告時(shí)間：2025年11月8日（周六）上午9：00

報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓304會(huì)議室

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

報(bào)告人簡(jiǎn)介：

高云石，安徽師范大學(xué)講師，研究方向?yàn)殡S機(jī)過(guò)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(guó)家自然科學(xué)基金青年項(xiàng)目1項(xiàng)。

報(bào)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.