中科院随机分析中心概率讨论班

时间: 2026年3月20日（周五） 15：00-16：00
地点: 南楼613
报告人: 冯媛媛（华东师范大学）
题目: Speeding up Langevin Dynamics by Mixing
摘要: In this talk, we would study how stirring would help dissipate the energy and the applications, especially the application to the Langevin dynamics. We would first introduce the dissipation enhancing flows and study the dissipation time of such flows, where the dissipation time is explicitly computed based on the mixing rate. We then use mixing velocity field as a drift added to the Langevin dynamics (without changing the stationary distribution) and obtain quantitative estimates on the convergence rate of the system. We show that an exponentially mixing drift can be rescaled to make the mixing time of the Langevin system arbitrarily small.

时间: 2026年3月20日（周五） 16：00-17：00
地点: 南楼613
报告人: 苏厚齐（首都师范大学）
题目: On the stability of rarefaction for stochastic viscous conservation law
摘要: This talk investigates the asymptotic stability of rarefaction waves for stochastic viscous conservation laws driven by nonlinear conservative noise. This regime involves a critical scaling where stochastic fluctuations are of the same order as viscous dissipation. While kinetic and viscosity solution frameworks have been successful in other contexts, bridging the gap to the high-order regularity required for this specific stability analysis remains a challenge.} To address this, we develop a three-part approach \begin{enumerate} \item A {Stochastic Area Inequality} to control accumulated energy fluctuations; \item A {stochastic $\rm{L_{loc}^{1}}$ contraction principle} (via the Kružkov doubling-of-variables) to establish uniqueness for non-integrable profiles; \item A {modified Galerkin approximation} to preserve the {\rm{$H^2$}} energy structure. \end{enumerate} Our analysis first establishes a general rigidity result: provided the solution maintains regularity, it asymptotically converges to the rarefaction wave. Furthermore, we prove the global well-posedness for small initial perturbations. Notably, the critical competition between noise and dissipation suggests that this smallness condition reflects a physical threshold for stability rather than a purely technical limitation.

时间: 2026年4月3日（周五） 15：00-16：00
地点: 南楼613
报告人: 贾晨（北京计算科学研究中心）
题目: 复杂生化反应网络的随机理论
摘要: 细胞中的生化反应网络与基因调控网络是复杂系统的典型代表，是具有高度非线性与随机性的多层次动态网络。深入揭示生化反应网络的随机动力学与热力学规律，不仅有助于阐明细胞命运决定与疾病发生发展等重要问题的内在机制，也为复杂系统研究提供了可借鉴的新型理论范式，相关研究已成为国际上数学、物理学、生物学、化学、统计学、智能科学的前沿交叉领域之一。我将介绍我与合作者在这方面的最新研究成果，希望能起到抛砖引玉的作用。

时间: 2026年4月3日（周五） 16：00-17：00
地点: 南楼613
报告人: Chevalier Guillaume（中科院应用所）
题目: Hitting Probabilities for Finite-Range Random Walks on Infinite Trees
摘要: When we consider a random walk on an infinite tree, it is natural to ask how the sequence of probabilities that such a random walk is in a given subset of vertices after a certain among of steps, behaves when the number of steps goes to infinity. In this talk, I will present a method for obtaining asymptotic expansions to any order for such sequence of probabilities, improving a result due to S. P. Lalley(Ann. Probab. 21 (1993), no. 4, p.2087-2130). More precisely, if $x,y$ are two vertices of an infinite, locally finite tree in which every vertex has at least three neighbours, and if $(Z_n)_n$ denotes an irreducible finite range random walk on the tree, based at $x$, whose transition kernel is invariant under a cofinite action of an automorphism group of the tree, then there exist constants $r\in\mathbb{Z}/d\mathbb{Z}$, $C>0$ and $(c_l)_{l\geq 1}$ such that we have the asymptotic expansion: $$\mathbb{P}^x(Z_{dn+r}\in \{y\})\sim_\infty \frac{C}{R^{dn} n^{3/2}}\left( 1 + \sum_{l\geq 1} \frac{c_{l}}{n^{l}}\right),$$ and $\mathbb{P}^x(Z_{dn+t}=y)=0$ for any $t\neq r \, [d]$, with $d$ the period of the random walk and $R>1$ the radius of convergence of the associated generating function called Green's function. We will also see that such analogous asymptotic holds \textit{mutatis mutandis}, almost surely when we replace $\{y\}$ by a geodesic ray, or a horocycle for nearest-neighbour random walks.

时间: 2026年4月17日（周五） 15：00-16：00
地点: 南楼613
报告人: 林棽（巴黎索邦大学）
题目: Discrete orthogonal polynomial ensembles have attracted much attention in recent years due to their connections to combinatorial probability models such as the Aztec diamond model, domino tilings, and random increasing subsequences. Motivated by these examples, several discrete beta-ensembles have been constructed using gamma functions and symmetric functions. In this talk, I will present concrete examples for β = 1 and β = 4, and if time permits, I will discuss a possible two-component discrete log-gas.
摘要: We study the critical branching random walk on Z^d started from a distant point x and conditioned to hit some compact set K in Z^d. We are interested in the occupation time in K and present its asymptotic behaviors in different dimensions. It is shown in this work that the occupation time is of order ||x||^{4−d} in dimensions d≤3, of order log ||x|| in dimension d=4, and of order 1 in dimensions d≥5. The corresponding weak convergences are also established. These results answer a question raised by Le Gall and Merle (Elect. Comm. in Probab. 11 (2006), 252–265). This is a joint work with Xinxin Chen (Beijing Normal University), available at https://arxiv.org/abs/2512.24047.

时间: 2026年4月17日（周五） 16：00-17：00
地点: 南楼613
报告人: 李石虎（江苏师范大学）
题目: Some recent results on SPDEs with nonlinear multiplicative noise
摘要: In this talk, we will discuss some recent process on SPDEs with nonlinear multiplicative noise. In particular, we obtain the global existence, uniqueness for stochastic 3D Navier-Stokes equations. Moreover,we also investigate the existence and uniqueness of invariant measures for stochastic 3D Navier-Stokes equations.

时间: 2026年4月29日（周三） 15：00-16：00
地点: 南楼613
报告人: 李世豪（四川大学）
题目: On several discrete ensembles
摘要: Discrete orthogonal polynomial ensembles have attracted much attention in recent years due to their connections to combinatorial probability models such as the Aztec diamond model, domino tilings, and random increasing subsequences. Motivated by these examples, several discrete beta-ensembles have been constructed using gamma functions and symmetric functions. In this talk, I will present concrete examples for β = 1 and β = 4, and if time permits, I will discuss a possible two-component discrete log-gas.

时间: 2026年4月29日（周三） 16：00-17：00
地点: 南楼613
报告人: 魏菲（北京邮电大学）
题目: 经典群上 Haar 随机矩阵特征多项式导数的联合矩问题
摘要: 在本次报告中，我将首先介绍酉群、酉辛群和正交群上服从 Haar 分布的随机矩阵特征多项式导数联合矩问题的研究背景；随后介绍该问题的研究进展，并重点介绍本人近期在酉辛群和正交群情形下取得的相关结果，以及该问题与一类重要的非线性二阶微分方程Painlevé方程解之间的联系。本报告内容基于我最近与合作者 Assiotis、Gunes 和 Keating 发表在 Proceedings of the London Mathematical Society（132(3), e70136, 2026）上的研究成果。

时间: 2026年5月12日（周二） 10：30-11：30
地点: 南楼620
报告人: 黄辉（湖南大学）
题目: A study of the classical consensus‑based optimization model
摘要: Consensus‑based optimization (CBO) is a relatively recent class of particlebased methods for global optimization, inspired by collective behavior in nature and rooted in stochastic dynamics. In this talk, we introduce the classical CBO model, where a swarm of agents iteratively updates their positions under the influence of attraction to a weighted consensus point and random perturbations. We present the mathematical formulation of the CBO model and discuss its key features. In particular, we shall establish its global convergence in mean‑field law toward the global minimizer of a given objective function under suitable assumptions.

时间: 2026年5月22日（周五） 15：00-16：00
地点: 南楼613
报告人: 刘伟华（浙江大学）
题目: TBA
摘要: TBA

时间: 2026年5月22日（周五） 16：00-17：00
地点: 南楼613
报告人: 黄凤麟（北京大学）
题目: TBA
摘要: TBA

时间: 2026年5月29日（周五） 15：00-16：00
地点: 南楼613
报告人: 郝子墨（北京理工大学）
题目: TBA
摘要: TBA

时间: 2026年5月29日（周五） 16：00-17：00
地点: 南楼613
报告人: 洪伟（江苏师范大学）
题目: TBA
摘要: TBA

时间: 2026年6月5日（周五） 15：00-16：00
地点: 南楼613
报告人: 巩舒阳（北京大学）
题目: TBA
摘要: TBA

时间: 2026年6月5日（周五） 16：00-17：00
地点: 南楼613
报告人: 李章颂（北京大学）
题目: TBA
摘要: TBA

时间: 2026年6月12日（周五） 15：00-16：00
地点: 南楼613
报告人: 唐鹏飞（天津大学）
题目: TBA
摘要: TBA

时间: 2026年6月12日（周五） 16：00-17：00
地点: 南楼613
报告人: 李文博（清华大学）
题目: TBA
摘要: TBA

时间: 2026年6月18日（周四） 15：00-16：00
地点: 南楼613
报告人: 王敏（武汉理工大学）
题目: TBA
摘要: TBA

时间: 2026年6月26日（周五） 16：00-17：00
地点: 南楼613
报告人: Emmanuel Jacob（ENS Lyon）
题目: TBA
摘要: TBA