Palm pairs and the general mass-transport principle

幺模随机测度度量空间及其上的Palm理论

Unimodular Random Measured Metric Spaces and Palm Theory on Them

本文定义了幺模随机测度度量空间作为多种离散与非离散概念的共同推广，证明了弱极限、随机游走等一般性结果，并将Palm理论推广至该空间以简化计算。

Invariant transports of stationary random measures and mass-stationarity

We introduce and study invariant (weighted) transport-kernels balancing stationary random measures on a locally compact Abelian group. The first main result is an associated fundamental invariance property of Palm measures, derived from a generalization of Neveu's exchange formula. The second main result is a simple sufficient and necessary criterion for the existence of balancing invariant transport-kernels. We then introduce (in a nonstationary setting) the concept of mass-stationarity with respect to a random measure, formalizing the intuitive idea that the origin is a typical location in t…

平稳随机测度间输运距离的 Benamou-Brenier 公式

A Benamou-Brenier formula for transport distances between stationary random measures

本文为平稳随机测度间的 Wasserstein 度量推导出 Benamou-Brenier 型动力学公式，关键创新在于利用 Palm 概率重新表述该度量。

Stable transports between stationary random measures

We give an algorithm to construct a translation-invariant transport kernel between ergodic stationary random measures $Φ$ and $Ψ$ on $\mathbb R^d$, given that they have equal intensities. As a result, this yields a construction of a shift-coupling of an ergodic stationary random measure and its Palm version. This algorithm constructs the transport kernel in a deterministic manner given realizations $φ$ and $ψ$ of the measures. The (non-constructive) existence of such a transport kernel was proved in [8]. Our algorithm is a generalization of the work of [3], in which a construction is provided …

平稳随机测度的不变输运：渐近方差、超均匀性与实例

Invariant transports of stationary random measures: asymptotic variance, hyperuniformity, and examples

本文研究平稳随机测度不变输运的渐近方差保持条件，利用阶乘矩展开和停止集技术建立混合准则，并构造超均匀化器将任意有限强度遍历点过程转化为超均匀过程。

Extended Mean Field Control Problems: stochastic maximum principle and transport perspective

We study Mean Field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic maximum principle, both in necessary and in sufficient form, which extend the known conditions to this general framework. Furthermore, we suggest a variational approach to study a weak formulation of these control problems. We show a natural connection between this weak formulation and optimal transport on path space, which inspires a novel discretization scheme.