Research output: Contribution to journal › Article › peer-review
Universal adic approximation, invariant measures and scaled entropy. / Vershik, A. M.; Zatitskii, P. B.
In: Izvestiya Mathematics, Vol. 81, No. 4, 01.01.2017, p. 734-770.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Universal adic approximation, invariant measures and scaled entropy
AU - Vershik, A. M.
AU - Zatitskii, P. B.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - We define an infinite graded graph of ordered pairs and a canonical action of the group ℤ (the adic action) and of the infinite sum of groups of order two D = Σ∞1 ℤ/2ℤ on the path space of the graph. It is proved that these actions are universal for both groups in the following sense: every ergodic action of these groups with invariant measure and binomial generator, multiplied by a special action (the 'odometer'), is metrically isomorphic to the canonical adic action on the path space of the graph with a central measure. We consider a series of related problems.
AB - We define an infinite graded graph of ordered pairs and a canonical action of the group ℤ (the adic action) and of the infinite sum of groups of order two D = Σ∞1 ℤ/2ℤ on the path space of the graph. It is proved that these actions are universal for both groups in the following sense: every ergodic action of these groups with invariant measure and binomial generator, multiplied by a special action (the 'odometer'), is metrically isomorphic to the canonical adic action on the path space of the graph with a central measure. We consider a series of related problems.
KW - Adic transformation
KW - Graph of ordered pairs
KW - Scaled entropy
KW - Universal action
UR - http://www.scopus.com/inward/record.url?scp=85029726975&partnerID=8YFLogxK
U2 - 10.1070/IM8610
DO - 10.1070/IM8610
M3 - Article
AN - SCOPUS:85029726975
VL - 81
SP - 734
EP - 770
JO - Izvestiya Mathematics
JF - Izvestiya Mathematics
SN - 1064-5632
IS - 4
ER -
ID: 36194551