论文标题
衡量标准的扩散：具有碰撞的粒子系统及其应用
A measure-on-graph-valued diffusion: a particle system with collisions, and their applications
论文作者
论文摘要
研究了带有顶点集$ v $，$ \ sum_ {i \ in V}x_iΔ_i$的概率度量的扩散。每个顶点上的质量满足表格的随机微分方程，$ dx_i = \ sum_ {j \ in N（i）} \ sqrt {x_ix_jj} db_ {ij} $ on sistemx上的db_ {ij} $，其中$ \ \ \ {b_ {b_ {ij} \ n sys $ issy n s $ iss $ is symian and ske and ske and ske and ske a ske and skew and a skew and skew of skew and skew of skew and a skew a skew and a skew a skew顶点$ i $。与扩散相关的Markov Semigroup的整数分区上的双马尔可夫链用于表明伴随半群的极端固定状态的支持是该图的独立集。我们还通过线性漂移研究了扩散，从而在有限的整数晶格上杀死了双马可夫链。马尔可夫链用于研究扩散的唯一固定状态，该状态概括了差异分布。讨论了扩散的两种应用：分析算法以找到独立的图集，以及基于样品概率的计算，通过使用过去的耦合来计算样品的概率。
A diffusion taking value in probability measures on a graph with a vertex set $V$, $\sum_{i\in V}x_iδ_i$, is studied. The masses on each vertices satisfy the stochastic differential equation of the form $dx_i=\sum_{j\in N(i)}\sqrt{x_ix_j}dB_{ij}$ on the simplex, where $\{B_{ij}\}$ are independent standard Brownian motions with skew symmetry and $N(i)$ is the neighbour of the vertex $i$. A dual Markov chain on integer partitions to the Markov semigroup associated with the diffusion is used to show that the support of an extremal stationary state of the adjoint semigroup is an independent set of the graph. We also investigate the diffusion with a linear drift, which gives a killing of the dual Markov chain on a finite integer lattice. The Markov chain is used to study the unique stationary state of the diffusion, which generalizes the Dirichlet distribution. Two applications of the diffusions are discussed: analysis of an algorithm to find an independent set of a graph, and a Bayesian graph selection based on computation of probability of a sample by using coupling from the past.
