论文标题
随机简单集
Randomized simplicial sets
论文作者
论文摘要
我们构建了新的几何实现，以简单的和简化的套件来实现，其中标准的$ n $ simplex被视为$ n+1 $元素的概率度量的空间，被$（n+1）$的空间替换为$（n+1）$的随机变量，并带有概率转化的拓扑结构。我们证明，将其与随机变量相关联的地图是其概率定律是从这些新的几何实现到经典的概率等效性。最后，我们证明这种实现在简单集和拓扑空间之间提供了新的Quillen等效性。
We construct new geometric realizations of simplicial and pre-simplicial sets where the standard $n$-simplex, viewed as the space of probability measures on $n+1$ elements, is replaced by the space of $(n+1)$-valued random variables, with the topology of probability convergence. We prove that the map which associates to a random variable its probability law is an homotopy equivalence from these new geometric realizations to the classical ones. Finally, we prove that this realization provides a new Quillen equivalence between simplicial sets and topological spaces.
