Dobrushin and Steif Metrics are Equal Dobrushin and Steif Metrics are Equal

It is proved here that two useful and apparently different metrics on the set of Borel probabilities on countable products of Polish spaces of bounded diameters are equal. This tidies up the subject and paves the way for advances in their computation, because one is defined as a supremum and the oth...

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Bibliographic Details
Published inJournal of theoretical probability Vol. 38; no. 3
Main Authors Armstrong-Goodall, Jacob A., MacKay, Robert S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2025
Springer Nature B.V
Subjects
Cellular automata
Infimum
Majority voters
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
90C46
Metric
Polish space
60J05
54E70
Multivariate
Borel probability
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Summary:It is proved here that two useful and apparently different metrics on the set of Borel probabilities on countable products of Polish spaces of bounded diameters are equal. This tidies up the subject and paves the way for advances in their computation, because one is defined as a supremum and the other as an infimum. As an example of application, the distance between two stationary probabilities for Toom’s north–east–centre majority voter probabilistic cellular automaton is calculated exactly.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-025-01438-5