Extremal clustering under moderate long range dependence and moderately heavy tails

带奇异相互作用与环境噪声的中等相互作用粒子系统的标度极限

Scaling Limit of Moderately Interacting Particle Systems with Singular Interaction and Environmental Noise

本文研究带奇异相互作用核与环境噪声的中等相互作用粒子系统，证明软化经验测度强收敛于非线性Fokker-Planck方程唯一局部解，方法适用于Biot-Savart和排斥Poisson核。

极端长程依赖下的中等重尾极值

Moderately Heavy Extreme Values under Extreme Long Range Dependence

本文研究边际尾部为次指数且属于Gumbel最大值吸引域的平稳序列，针对极端长程依赖导致的极值由多个大值引起并呈分形聚集的现象，建立了具有非Gumbel极限对象的函数型极值极限定理。

A New Shape of Extremal Clusters For Certain Stationary Semi-Exponential Processes With Moderate Long Range Dependence

Extremal clusters of stationary processes with long memory can be quite intricate. For certain stationary infinitely divisible processes with subexponential tails, including both power-like tails and certain lighter tails, e.g. lognormal-like tails, such clusters may take the shape of stable regenerative sets. In this paper we show that for semi-exponential tails, which are even lighter, a new shape of extremal clusters arises. In this case each stable regenerative set supports a random panoply of varying extremes.

Rigorous derivation of population cross-diffusion systems from moderately interacting particle systems

Population cross-diffusion systems of Shigesada-Kawasaki-Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion term in the stochastic model depends nonlinearly on the interactions between the individuals, and the drift term is the gradient of the environmental potential. In the first step, the mean-field limit leads to an intermediate nonlocal model. The local cross-diffusion system is derived in the second step in a moderate scaling regime, when the interaction potent…

大型手性非厄米随机矩阵极值特征值的偏差与中偏差

Deviation and moderate deviation for extremal eigenvalues of large Chiral non-Hermitian random matrices

本文研究了带参数 $n$ 和 $v$ 的大型手性非厄米随机矩阵系综，建立了其谱半径及相关极值特征值平方的偏差概率与中偏差概率。