浙江大学---复旦大学概率统计联合讨论班
时间：2019年4月20日
地点：浙江大学玉泉校区欧阳纯美楼316
上午 主持人： 苏中根 浙江大学
题目：The Brownian net and its universality
11:00-11:45 孙文杰 复旦大学
题目: An introduction to scaling limit, conditional LERW and
SKLE
下午 主持人：应坚刚 复旦大学
14:00-14:45 吴波 复旦大学
题目：Functional inequality, stochastic heat equation and Ricci flow
15:00-15:45 赵敏智 浙江大学
题目：On the distribution of the hitting time for the N-urn Ehrenfest model
欢迎大家参加！
联系人：赵敏智 zhaomz@zju.edu.cn
The Brownian net and its universality
俞锦炯
Universality is the observation that a large class of random systems share a set of universal laws, while the systems differ in many details. The Brownian net, loosely speaking, is a collection of branching and coalescing Brownian motions starting from every space-time point. It is expected to give rise to a universality class for one dimensional interacting particle systems with branching-coalescence. We aim to verify this universal property by identifying weak limits of a class of non-simple random walks. This is based on joint work with Rongfeng Sun and Jan M. Swart.
An introduction to scaling limit, conditional LERW and SKLE
孙文杰
Schramm-Loewner evolution (SLE) is a conformally invariant process with domain Markov property in a simple connected planar domain. SLE has been proved or conjectured to be the scaling limit of many discrete models in statistical mechanics, such as the loop-erased random walk (LERW). In this talk I will give a brief introduction to SLE and LERW, and their generalizations in multiply connected domains, which are called stochastic Komatu-Loewner evolution (SKLE) and conditional LERW respectively.
Functional inequality, stochastic heat equation and Ricci flow
Functional Inequality, Stochastic Heat Equation and Ricci Flow in a Riemannian manifold are three important directions in Mathematical research. In this talk, we will first introduce the recent development of functional inequalities on path space over a Riemannian manifold. Next, we will discuss the stochastic heat equations in a manifold and related results. Finally, the close connection between functional inequality and stochastic heat equation and Ricci flow will discussed.
On the distribution of the hitting time for the N-urn Ehrenfest model
赵敏智
In this paper, we consider the N-urn Ehrenfest model. By utilizing an auxiliary continuous--time Markov chain, we get the explicit formula for the Laplace transform of the hitting time from a single state to a set A of states where A satisfies some symmetric properties. After obtaining the Laplace transform, we are able to compute the high--order moments (especially, variance) for the hitting time.