q-EXCHANGEABILITY VIA QUASI-INVARIANCE
成果类型：
Article
署名作者：
Gnedin, Alexander; Olshanskii, Grigori
署名单位：
Utrecht University; Kharkevich Institute for Information Transmission Problems of the RAS
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/10-AOP536
发表日期：
2010
页码：
2103-2135
关键词：
摘要：
For positive q not equal 1, the q-exchangeability of an infinite random word is introduced as quasi-invariance under permutations of letters, with a special cocycle which accounts for inversions in the word. This framework allows us to extend the q-analog of de Finetti's theorem for binary sequences-see Gresehonig and Schmidt [Colloq. Math. 84/85 (2000) 495-514]-to general real-valued sequences. In contrast to the classical case of exchangeability (q = 1), the order on R plays a significant role for the q-analogs. An explicit construction of ergodic q-exchangeable measures involves random shuffling of N = {1, 2,...} by iteration of the geometric choice. Connections are established with transient Markov chains on q-Pascal pyramids and invariant random flags over the Galois fields.