Convergence of the quantile admission process with veto power

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Feldheim, Naomi Dvora¹  Feldheim, Ohad Noy² 

[1] Bar Ilan Univ, Ramat Gan, Israel

[2] Hebrew Univ Jerusalem, Jerusalem, Israel

关键词: Social groups;    Admission process;    Evolving sets;    Random walk in changing environment;   

DOI  :  10.1016/j.spa.2019.12.005

来源: Elsevier

【 摘 要 】

The quantile admission process with veto power is a stochastic process suggested by Alon, Feldman, Mansour, Oren and Tennenholtz as a model for the evolution of an exclusive social club. Each member is represented by a real number (his opinion). On every round two new candidates, holding i.i.d. mu-distributed opinions, apply for admission. The one whose opinion is minimal is then admitted if the percentage of current members closer in their opinion to his is at least r; otherwise, neither is admitted. We show that for any mu and r, the empirical distribution of opinions in the club converges a.s. to a limit distribution. We further analyse this limit, show that it may be non-deterministic and provide conditions under which it is deterministic. The results rely on a coupling of the evolution of the empirical r-quantile of the club with a random walk in a changing environment. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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