论文标题
随机地图的物理措施有限
Finitude of physical measures for random maps
论文作者
论文摘要
对于在波兰空间上独立且相同分布的可测量图的随机组成，我们研究了绝对连续的ergodic固定概率度量（尤其是物理措施）的存在和限制，其吸引力的盆地几乎覆盖了整个空间。我们根据其关联的Markov运算符来表征和层层化此类随机地图，并通过大量示例（包括加性噪声，乘法噪声和迭代功能系统）显示了层次结构中类之间的差异。我们还提供了足够的实际条件，使随机地图属于这些类别。例如，我们确定在紧凑的Riemannian歧管上具有绝对连续过渡概率的任何连续随机图具有有限的许多物理测量，其吸引力的盆地涵盖了Lebesgue几乎所有的歧管。
For random compositions of independent and identically distributed measurable maps on a Polish space, we study the existence and finitude of absolutely continuous ergodic stationary probability measures (which are, in particular, physical measures) whose basins of attraction cover the whole space almost everywhere. We characterize and hierarchize such random maps in terms of their associated Markov operators, as well as show the difference between classes in the hierarchy by plenty of examples, including additive noise, multiplicative noise, and iterated function systems. We also provide sufficient practical conditions for a random map to belong to these classes. For instance, we establish that any continuous random map on a compact Riemannian manifold with absolutely continuous transition probability has finitely many physical measures whose basins of attraction cover Lebesgue almost all the manifold.
