Mini-Workshop on Probability and Related Topics

发布时间:2021年09月24日 作者:刘源远   阅读次数:[]





报告题目:Random distances of Liouville quantum gravity: recent and very recent progresses

报 告 人:丁剑 宾夕法尼亚大学

报告摘要:In this talk I will review some recent and very recent progress on random metric associated with Liouville quantum gravity with focus on the construction and the phase transition. The talk is based on works with Julien Dubédat, Alexander Dunlap, Hugo Falconet, Subhajit Goswami, Ewain Gwynne, Avelio Sepúlveda, Ofer Zeitouni and Fuxi Zhang in various combinations, and especially on a few very recent joint works with Ewain Gwynne.

报告人简介:丁剑,现任宾夕法尼亚大学Gilbert Helman讲席教授。2006年获北京大学学士学位,2011年获加州大学伯克利分校博士学位。曾获2015年度斯隆研究奖,2017年度戴维逊奖。主要研究领域是概率论,尤其关注统计物理学与计算机科学的交叉,相关成果发表在Acta Math., Ann. Math.,Invent. Math,CMP,CPAM,AOP,PTRF等数学和概率顶级学术期刊上。



报告题目:Hitting probability of Gaussian random fields and collision of eigenvalues of random matrices

报 告 人:宋健 山东大学

报告摘要:Let X = {X(t), t∈ RN } be a centered Gaussian random field with values in Rd and let F\in Rd\{0} be a Borel set. We provide a sufficient condition for F to be polar for X, i.e., P( X(t)∈F) for some t∈ RN ) = 0. By applying this condition, we solve a problem on the existence of collisions of the eigenvalues of random matrices with Gaussian random field entries in critical dimension that was left open in [Jaramillo-Nualart (2020)] and [Song-Xiao-Yuan (2021)]. This talk is based on joint works with Cheuk-Yin Lee, Yimin Xiao, and Wangjun Yuan.

报告人简介:宋健,山东大学教授。2010年美国堪萨斯大学博士,2010-2012美国罗格斯大学博士后,2013-2018香港大学助理教授。主要从事随机偏微分方程、随机矩阵、统计物理模型等方面的研究,成果发表在AOP, JFA, AAP,SIMA, EJP, Bernoulli, AIHP, SPA等高水平学术期刊上。






报告题目:Two-time-scale Regime-switching Stochastic Kolmogorov Systems with Wideband Noises

报 告 人:温哲鑫 中南大学

报告摘要:In our recent work, in lieu of using white noise, we examined Kolmogorov systems driven by wideband noise. Such systems naturally arise in statistical physics, biological and ecological systems, and many related fields. One of the motivations of our study is to treat more realistic models than the usually assumed stochastic differential equation models. The rationale is that a Brownian motion is an idealization used in a wide range of models, whereas wideband noise processes are much easier to be realized in the actual applications. This paper further investigates the case that in addition to the wideband noise process, there is a singularly perturbed Markov chain. The added Markov chain is used to model discrete events. Although it is a more realistic formulation, because of the non-Markovian formulation due to the wideband noise and the singularly perturbed Markov chain, the analysis is more difficult. Using weak convergence methods, we obtain a limit result. Then we provide several examples for the utility of our findings. This talk is based on a joint work with Professor George Yin [University of Connecticut].

报告人简介:温哲鑫,中南大学数学与统计学院博士后。2021年于美国Wayne State University获得博士学位。主要从事随机微分方程及随机控制的相关研究。成果发表Phys. A, JSSC, ARM等杂志上。



报告题目:Hausdorff dimensions of multiple points on the boundaries of Brownian loop-soup clusters

报 告 人:高一帆 北京大学

报告摘要:We establish the up-to-constants estimates for generalized disconnection probabilities introduced in [Qian 2021], then use this to show that the Hausdorff dimensions of multiple points on the boundaries of Brownian loop-soup clusters are related to the corresponding generalized disconnection exponents. Combining with exact values of such exponents computed in [Qian 2021], we obtain the exact Hausdorff dimensions of multiple points on cluster boundaries. This talk is based on a joint work with Xinyi Li and Wei Qian.




报告题目:Gromov-Hausdorff-Prokhorov convergence of vertex cut-trees of n-leaf Galton-Watson trees

报 告 人:何辉 北京师范大学

报告摘要:We study the vertex cut-trees of Galton-Watson trees conditioned to have n leaves. This notion is a slight variation of Dieuleveut’s vertex cut-tree of Galton-Watson trees conditioned to have n vertices. Our main result is a joint Gromov-Hausdorff-Prokhorov convergence in the finite variance case of the Galton-Watson tree and its vertex cut-tree to Bertoin and Miermont’s joint distribution of the Brownian CRT and its cut-tree. The methods also apply to the infinite variance case, but the problem to strengthen Dieuleveut’s and Bertoin and Miermont’s Gromov-Prokhorov convergence to Gromov-Hausdorff-Prokhorov remains open for their models conditioned to have n vertices. This is a joint work with Matthias Winkel.

报告人简介:何辉,北京师范大学教授。2008年博士毕业于北京师范大学,于2009-2010年在法国奥尔良大学从事博士后研究。主要从事分枝过程及相关随机树理论的研究,成果发表在PTRF, Bernoulli, AIHP, SPA等高水平学术期刊上。



报告题目:Entropic repulsion phenomena for Random Interlacements

报 告 人:李欣意 北京大学

报告摘要:The model of random interlacements is the Poissonian collection of doubly-infinite random-walk-like trajectories in Z^d, d \geq 3. Originally introduced by Sznitman in 2007, this model has received a lot of attention among the probabilist community. In this talk, we discuss some entropic repulsion phenomena that emerged from the study of random interlacements. This is a joint work with Zijie Zhuang (PKU).







报告题目:Fixed points for branching Brownian motions

报 告 人:陈昕昕 北京师范大学

报告摘要:We consider a particle system by attaching to each atom of some point process \theta an independent branching Brownian motions (BBM) with critical drift and study all point processes which are left invariant. with some random shift. Under the assumption that \theta(\R_+)<\infty a.s., We show that all fixed points are distributed as the extremal point process of BBM. This is a joint work with C. Garban and A. Shekhar (University Claude Bernard Lyon 1)

X. CHEN (Beijing Normal University).

报告人简介:陈昕昕,即将入职北京师范大学。2014年于巴黎六大获得博士学位,2014-2021就职于里昂一大。主要从事分支随机游走以及相关模型的研究,成果发表于PTRF, AIHP, SPA, EJP等高水平学术期刊上。

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