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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Random phase approximation for the mean-field electron gas （3）
平均场 电子气 随机相位近似
2023/11/29
Random phase approximation (RPA) was proposed by Bohm and Pines in four seminal papers during 1951-1953 to describe the correlation of fermions, namely the correction to the Hartree-Fock theory. While...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent developments on random hyperbolic surfaces of large genus
大属随机 双曲曲面 球面几何
2023/4/21
In this talk, we report several very recent asymptotic results on certain classical geometric quantities viewed as random variables on the moduli space of Riemann surfaces for large genus (and many cu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Random Surface, Planar Lattice Model, and Conformal Field Theory
随机曲面 平面晶格模型 共形场论
2023/4/13
Liouville quantum gravity (LQG) is a theory of random surfaces that originated from string theory. Schramm Loewner evolution (SLE) is a family of random planar curves describing scaling limits of many...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Learning Quantum Observables of Low Degrees from a Logarithmic Number of Random Queries
对数 随机查询 低次量子 可观察量
2023/4/14
A fundamental problem from computational learning theory is to well-reconstruct an unknown function on the discrete hypercubes. One classical result of this problem for the random query model is the l...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Branching random walks driven by products of random matrices
随机矩阵 乘积驱动 分支随机 游走
2023/4/18
A branching random walk is a system of particles, where each particle gives birth to new particles of the next generation, which move on $\mathbb R^d$ according to some probability law. In this talk, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multitype branching processes in random environments
随机环境 多类型 分支进程
2023/4/18
We consider a branching process with a random environment, in which the reproduction law of generation $n$ depends on the random environment at time n, unlike a constant distribution assumed in the cl...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Products of random matrices
随机矩阵 乘积 极限定理收敛率
2023/4/19
Let $(g_n)_{n\geq 1}$ be a sequence of independent and identically distributed random matrices of type $d \times d $ with real coefficients. Consider the products $G_n : = g_n \ldots g_1$ and the rand...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dynamics of a Nutrient-Phytoplankton Model with Random Phytoplankton Mortality
随机浮游植物死亡率 营养-浮游植物 模型动力学
2023/4/28
In this talk, we investigate a stochastic nutrient-phytoplankton model which incorporates the effect of white noise on phytoplankton growth. The global existence and uniqueness of a positive solution,...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements IV: the entropic repulsion phenomenon and other types of large deviations
随机交错 大偏差 熵斥力现象 大偏差
2023/5/8
In this lecture, I will talk about how to control the deviation of the occupation-time profile conditioned on disconnection so that this conditioning makes the model exhibit a phenomenon generally kno...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements III: Disconnection probabilities for random interlacements
随机交错 大偏差 随机交错 断开概率
2023/5/8
In this lecture, I will discuss how ``tilted interlacements’’ and ``solidification of porous surfaces’’, two specific realizations of the change-of-measure and coarse graining ideas respectively, prod...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements II: tilted interlacements and solidification of porous surfaces
随机交错 大偏差 倾斜交错 多孔表面 固化
2023/5/10
In this lecture, I will discuss how tilting and coarse graining, two key ideas in modern probability, come into play in deriving respectively the lower and upper bounds of the asymptotic probability i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements I: Large deviation principle of occupation measures
随机交错 大偏差 占用措施 大偏差原则
2023/5/10
In this lecture, I will talk about the large deviation problems in random interlacements, in particular the LDP of the occupation measure, and discuss its relations to sharp asymptotic probabilities o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Connection probabilities for random-cluster model and uniform spanning treeConnection probabilities for random-cluster model and uniform spanning tree
随机 聚类模型 均匀生成树 连接概率
2023/5/16
Conformal invariance of critical lattice models in two-dimensional has been vigorously studied for decades. The first example where the conformal invariance was rigorously verified was the planar unif...