PushTASEP in inhomogeneous space

Space-time statistical solutions for an inhomogeneous chain of harmonic oscillators

We consider an one-dimensional inhomogeneous harmonic chain consisting of two different semi-infinite chains of harmonic oscillators. We study the Cauchy problem with random initial data. Under some restrictions on the interaction between the oscillators of the chain and on the distribution of the initial data, we prove the convergence of space-time statistical solutions to a Gaussian measure.

非碰撞时空非齐次马尔可夫链

Non-colliding space-time inhomogeneous Markov chains

针对一类可积时空非齐次马尔可夫链，建立了碰撞时间尾部概率的显式首阶渐近及定量误差界，并通过条件过程验证了局部推阻相互作用粒子系统中的预测。

线上空间非齐次三态量子游走的平稳测度：再探

Stationary Measures of Space-Inhomogeneous Three-State Quantum Walks on Line: Revisited

本文通过约化矩阵方法，在温和条件下研究了线上空间非齐次三态量子游走两个模型的平稳测度，推广了文献中的已有结果。

Law of Large Numbers for Semi-Markov inhomogeneous Random Evolutions on Banach spaces

Using backward propagators, we construct inhomogeneous Random Evolutions on Banach spaces driven by (uniformly ergodic) Semi-Markov processes. After studying some of their properties (measurability, continuity, integral representation), we establish a Law of Large Numbers for such inhomogeneous Random Evolutions, and more precisely their weak convergence - in the Skorohod space $D$ - to an inhomogeneous semigroup. A martingale characterization of these inhomogeneous Random Evolutions is also obtained. Finally, we present applications to inhomogeneous Lévy Random Evolutions.

非齐次第一行的半空间最后通行渗流

Half-space last passage percolation with inhomogeneous first row

该研究针对半空间中第一行非齐次的指数最后通行渗流模型，结合TASEP模型，推导了重标最后通行时间的极限分布，并给出半空间点到点最后通行时间的相关关键分析结果。

The diameter of Inhomogeneous random graphs

In this paper we study the diameter of Inhomogeneous random graphs $G(n,κ,p)$ that are induced by irreducible kernels $κ$. The kernels we consider act on separable metric spaces and are almost everywhere continuous. We generalize results known for the Erdős-Rényi model $G(n,p)$ for several ranges of $p$. We find upper and lower bounds for the diameter of $G(n,κ,p)$ in terms of the expansion factor and two explicit constants that depend on the behavior of the kernel over partitions of the metric space.

Inhomogeneous Levy processes in Lie groups and homogeneous spaces

We obtain a representation of an inhomogeneous Levy process in a Lie group or a homogeneous space in terms of a drift, a matrix function and a measure function. Because the stochastic continuity is not assumed, our result generalizes the well known Levy-Ito representation for stochastic continuous processes with independent increments in Euclidean spaces and the extension to Lie groups.

空间非齐次随机环境中分支随机游走的紧性

Tightness for branching random walk in a space-inhomogeneous random environment

针对整数集上空间非齐次随机环境中的分支随机游走，证明存在仅依赖环境的中心化项，使最大值经中心化后在退火意义下具有紧性。

Random cutout sets with spatially inhomogeneous intensities

We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal spaces using the multifractal decomposition of the average densities for the natural measures.

The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck Processes with Lévy Noise in Hilbert spaces

This paper is about the structure of all entrance laws (in the sense of Dynkin) for time-inhomogeneous Ornstein-Uhlenbeck processes with Lévy noise in Hilbert state spaces. We identify the extremal entrance laws with finite weak first moments through an explicit formula for their Fourier transforms, generalising corresponding results by Dynkin for Wiener noise and nuclear state spaces. We then prove that an arbitrary entrance law with finite weak first moments can be uniquely represented as an integral over extremals. It is proved that this can be derived from Dynkin's seminal work "Sufficient…

非齐次马尔可夫链的矩阵集中不等式

Matrix concentration inequalities for time-inhomogeneous Markov chains

针对非齐次马尔可夫链生成的厄米随机矩阵和的最大特征值，建立了Chernoff型界，并应用于Elo评分系统的分析。