A factor of i.i.d with uniform marginals and infinite clusters spanned by equal labels

关于具有分形支撑和均匀(d-1)维边缘的d-随机测度及相关结果

On d-stochastic measures with fractal support and uniform (d-1)-marginals, and related results

本文研究了具有均匀(d-1)维边缘的d-随机测度族，构造了具有分形支撑和完全依赖的测度，并证明了其支撑集的Hausdorff维度集的稠密性及测度集的稠密性。

具有均匀边际的整数分拆增长过程与分拆系综的等价性

Growing integer partitions with uniform marginals and the equivalence of partition ensembles

本文构造了整数分拆上具有均匀边际的马尔可夫增长过程，分析其跳跃概率的渐近行为以解释极限形状的形成，并利用该过程给出两个随机分拆系综等价的充分条件，进而证明奇偶部分计数渐近独立且极限分布不同。

Optimal Brownian Stopping between radially symmetric marginals in general dimensions

Given an initial (resp., terminal) probability measure $μ$ (resp., $ν$) on $\mathbb{R}^d$, we characterize those optimal stopping times $τ$ that maximize or minimize the functional $\mathbb{E} |B_0 - B_τ|^α$, $α> 0$, where $(B_t)_t$ is Brownian motion with initial law $B_0\sim μ$ and with final distribution --once stopped at $τ$-- equal to $B_τ\sim ν$. The existence of such stopping times is guaranteed by Skorohod-type embeddings of probability measures in "subharmoic order" into Brownian motion. This problem is equivalent to an optimal mass transport problem with certain constraints, namely t…

具有均匀(d-1)维边际的d维copula与（完全）独立的距离有多远？

How far are $d$-dimensional copulas with uniform $(d-1)$-marginals from (total) independence?

该研究针对具有均匀(d-1)维边际的d维copula族，分析其与d维乘积copula在两种度量下的距离，得出该族规模超出预期的结论。