caa a22 4500 605525919 CHVBK 20210128100800.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10958-015-2533-z doi (NATIONALLICENCE)springer-10.1007/s10958-015-2533-z Vershik A. St.Petersburg Department of Steklov Mathematical Institute, St.Petersburg, Russia aut Equipped Graded Graphs, Projective Limits of Simplices, and Their Boundaries [Elektronische Daten] [A. Vershik] In this paper, we develop a theory of equipped graded graphs (or Bratteli diagrams) and an alternative theory of projective limits of finite-dimensional simplices. An equipment is an additional structure on the graph, namely, a system of "cotransition” probabilities on the set of its paths. The main problem is to describe all probability measures on the path space of a graph with given cotransition probabilities; it goes back to the problem, posed by E. B. Dynkin in the 1960s, of describing exit and entrance boundaries for Markov chains. The most important example is the problem of describing all central measures, to which one can reduce the problems of describing states on AF-algebras or characters on locally finite groups. We suggest an unification of the whole theory, an interpretation of the notions of Martin, Choquet, and Dynkin boundaries in terms of equipped graded graphs and in terms of the theory of projective limits of simplices. In the last section, we study the new notion of "standardness” of projective limits of simplices and of equipped Bratteli diagrams, as well as the notion of "lacunarization.” Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/6(2015-09-01), 860-873 1072-3374 209:6<860 2015 209 10958 https://doi.org/10.1007/s10958-015-2533-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2533-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Vershik A. St.Petersburg Department of Steklov Mathematical Institute, St.Petersburg, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/6(2015-09-01), 860-873 1072-3374 209:6<860 2015 209 10958