论文标题
詹特法律过程的极限点具有绝对连续的分布
The limit point in the Jante's law process has an absolutely continuous distribution
论文作者
论文摘要
我们研究了Grinfeld，Volkov和Wade于2015年推出的共识形成的随机模型，后者称其为多维随机凯恩斯主义的选美比赛。该模型由肯纳伯格（Kennerberg）和沃尔科夫（Volkov）概括，后者将其概括称为詹特（Jante）的法律过程。我们考虑了模型的一个版本，其中可能的意见空间是$ \ Mathbb {r}^d $中的凸面$ \ Mathcal {B} $。 $ n $人口中的个人每个人都有$ \ Mathcal {B} $的（多维）意见。反复的是，与当前意见的质量中心最远的个人选择了一个新的意见，从$ \ Mathcal {b} $随机地进行了均匀抽样。肯纳伯格（Kennerberg）和沃尔科夫（Volkov）表明，从质量中心收敛到随机限制点的一组意见集。我们表明，极限意见的分布是连续的，因此证明了Grinfeld等人的命题3.2之后做出的猜想。
We study a stochastic model of consensus formation, introduced in 2015 by Grinfeld, Volkov and Wade, who called it a multidimensional randomized Keynesian beauty contest. The model was generalized by Kennerberg and Volkov, who called their generalization the Jante's law process. We consider a version of the model where the space of possible opinions is a convex body $\mathcal{B}$ in $\mathbb{R}^d$. $N$ individuals in a population each hold a (multidimensional) opinion in $\mathcal{B}$. Repeatedly, the individual whose opinion is furthest from the center of mass of the $N$ current opinions chooses a new opinion, sampled uniformly at random from $\mathcal{B}$. Kennerberg and Volkov showed that the set of opinions that are not furthest from the center of mass converges to a random limit point. We show that the distribution of the limit opinion is continuous, thus proving the conjecture made after Proposition 3.2 in Grinfeld et al.
