An application of Jacobi's elliptic functions to asymptotic probabilities for conformal restriction measures

$β$-Jacobi系综极值特征值的重要性采样

Importance Sampling for the Extremal Eigenvalue of $β$-Jacobi ensemble

本文针对超高维$β$-Jacobi系综极值特征值的尾部概率稀有事件，提出了精确近似与高效估计量，并通过数值模拟验证了该方法的高效性与准确性。

$β$-Jacobi 系综极值的尾部概率的渐近有效估计量

Asymptotically efficient estimators for tail probabilities of extremals of $β$-Jacobi ensembles

本文研究 $β$-Jacobi 系综极值的尾部概率，通过对系综应用拉伸与平移变换确保极值满足大偏差，构造出依赖于大偏差速率函数的估计量，刻画了不同假设下极值的大偏差与中偏差行为。

Central limit theorems for hyperbolic spaces and Jacobi processes on $[0,\infty[$

We present a unified approach to a couple of central limit theorems for radial random walks on hyperbolic spaces and time-homogeneous Markov chains on the positive half line whose transition probabilities are defined in terms of the Jacobi convolutions. The proofs of all results are based on limit results for the associated Jacobi functions. In particular, we consider the cases where the first parameter (i.e., the dimension of the hyperbolic space) tends to infinity as well as the cases $ϕ_{iρ-λ}^{(α,β)}(t)$ for small $λ$, and $ϕ_{iρ-nλ}^{(α,β)}(t/n)$ for $n\to\infty$. The proofs of all these …

概率测度空间中的时间最优问题

Time-optimal problem in the space of probabilities measures

本文研究了概率测度空间中连续方程的时间最优问题，推导了动态规划原理，并证明了价值函数的Kruzhkov变换为Hamilton-Jacobi方程的粘性解，同时建立了价值函数的Γ收敛性。

Hitting probabilities for general Gaussian processes

For a scalar Gaussian process $B$ on $\mathbb{R}_{+}$ with a prescribed general variance function $γ^{2}\left(r\right) =\mathrm{Var}\left(B\left(r\right) \right) $ and a canonical metric $\mathrm{E}[\left(B\left(t\right) -B\left(s\right) \right) ^{2}]$ which is commensurate with $γ^{2}\left(t-s\right) $, we estimate the probability for a vector of $d$ iid copies of $B$ to hit a bounded set $A$ in $\mathbb{R}^{d}$, with conditions on $γ$ which place no restrictions of power type or of approximate self-similarity, assuming only that $γ$ is continuous, increasing, and concave, with $γ\left(0\righ…

Laguerre 与 Jacobi β 系综中边缘特征值分布的计算

Computation of marginal eigenvalue distributions in the Laguerre and Jacobi $β$ ensembles

本文针对 Laguerre 和 Jacobi β 系综，提出递归程序精确计算边缘特征值分布，并揭示其在量子输运中 Landauer 电导分布等问题的应用价值。