规模不变性和效率在赛马场博彩市场的出现
Emergence of scale invariance and efficiency in a racetrack betting market
摘要：
本文研究了日本赛马协会中赛马等级与胜负结果之间关系的时间变化。马是根据赢的赌注分数排名。随着投票的进行，赛马在赢注分数轴上混合。我们看到获胜马$x_{1}$和失败马$x_{0}$的累积分布函数之间出现了标度不变关系。$x_{1}\propto x_{0}^α$在小赢注分数区域中成立。随着投票的进行，我们也看到了市场的效率。然而，收敛到有效状态不是单调的。选票分布的时间变化是复杂的。在分布扩散到一定程度后，选票恢复集中在受欢迎的马匹上。为了解释尺度不变性，我们引入了一个简单的投票模型。在一个“双”缩放限制，我们表明，确切的规模不变关系$x_{1}=x_{0}^α$持有在整个范围$0\le x_{0},x_{1}\le 1$。
英文摘要：
We study the time change of the relation between the rank of a racehorse in the Japan Racing Association and the result of victory or defeat. Horses are ranked according to the win bet fractions. As the vote progresses, the racehorses are mixed on the win bet fraction axis. We see the emergence of a scale invariant relation between the cumulative distribution function of the winning horse $x_{1}$ and that of the losing horse $x_{0}$. $x_{1}\propto x_{0}^α$ holds in the small win bet fraction region. We also see the efficiency of the market as the vote proceeds. However, the convergence to the efficient state is not monotonic. The time change of the distribution of a vote is complicated. Votes resume concentration on popular horses, after the distribution spreads to a certain extent. In order to explain scale invariance, we introduce a simple voting model. In a `double' scaling limit, we show that the exact scale invariance relation $x_{1}=x_{0}^α$ holds over the entire range $0\le x_{0},x_{1}\le 1$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
