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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...
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...
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...
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...
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, ...
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...
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...
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,...
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...
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...
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...
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...
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...
近日,数学学院2019级硕士研究生舒希超收到了来自理论计算机领域顶级会议SODA(ACM-SIAM Symposium of Discrete Algorithms)的论文录用信。舒希超与美国罗德岛大学的韩杰研究员和山大数学学院的王光辉教授合作的论文《Non-linear Hamilton cycles in linear quasi-random hypergraphs》将发表在2021年1月的...

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