论文标题
匹配随机系统，并应用最小的重量扩展
Matching for random systems with an application to minimal weight expansions
论文作者
论文摘要
我们将匹配的一维动力系统匹配的概念扩展到间隔的随机动态系统的随机匹配。我们证明，对于间隔的一系列分段仿射随机系统，随机匹配的属性意味着任何不变密度都是分段常数的。我们进一步介绍了一个随机动力学系统的单参数家族，该系统在间隔[-1,1]中产生数字的符号二进制扩展。这个家庭几乎每个参数都与Lebesgue随机匹配。我们用它来证明相关签名的二进制扩展中数字0的频率永远不会超过1/2。
We extend the notion of matching for one-dimensional dynamical systems to random matching for random dynamical systems on an interval. We prove that for a large family of piecewise affine random systems of the interval the property of random matching implies that any invariant density is piecewise constant. We further introduce a one-parameter family of random dynamical systems that produce signed binary expansions of numbers in the interval [-1,1]. This family has random matching for Lebesgue almost every parameter. We use this to prove that the frequency of the digit 0 in the associated signed binary expansions never exceeds 1/2.
