A. M. Vershik, “The Problem of Describing Central Measures on the Path Spaces of Graded Graphs”, Funktsional. Anal. i Prilozhen., 48:4 (2014), 26–46; Funct. Anal. Appl., 48:4 (2014), 256

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Funktsional'nyi Analiz i ego Prilozheniya, 2014, Volume 48, Issue 4, Pages 26–46
DOI: https://doi.org/10.4213/faa3166 (Mi faa3166)

This article is cited in 23 scientific papers (total in 24 papers)

The Problem of Describing Central Measures on the Path Spaces of Graded Graphs

A. M. Vershik^abc

^a Saint Petersburg State University
^b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
^c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow

Full-text PDF (433 kB) Citations (24)

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DOI: https://doi.org/10.4213/faa3166

Abstract: We suggest a new method for describing invariant measures on Markov compacta and on path spaces of graphs and, thereby, for describing characters of certain groups and traces of $AF$-algebras. The method relies on properties of filtrations associated with a graph and, in particular, on the notion of a standard filtration. The main tool is an intrinsic metric introduced on simplices of measures; this is an iterated Kantorovich metric, and the central result is that the relative compactness in this metric guarantees the possibility of a constructive enumeration of ergodic invariant measures. Applications include a number of classical theorems on invariant measures.

Keywords: invariant and central measures, projective limit of simplices, filtrations, intrinsic metric, uniform compactness.

Funding agency	Grant number
Russian Science Foundation	14-11-00581

Received: 08.08.2014

English version:
Functional Analysis and Its Applications, 2014, Volume 48, Issue 4, Pages 256–271
DOI: https://doi.org/10.1007/s10688-014-0069-5

Bibliographic databases:

Document Type: Article

UDC: 517.9

Language: Russian

Citation: A. M. Vershik, “The Problem of Describing Central Measures on the Path Spaces of Graded Graphs”, Funktsional. Anal. i Prilozhen., 48:4 (2014), 26–46; Funct. Anal. Appl., 48:4 (2014), 256–271

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This publication is cited in the following 24 articles:

Jevtic F.D., Timotijevic M., Zivaljevic R.T., “Polytopal Bier Spheres and Kantorovich-Rubinstein Polytopes of Weighted Cycles”, Discret. Comput. Geom., 65:4 (2021), 1275–1286
P. Nikitin, “The Absolute of the Comb Graph”, J Math Sci, 247:5 (2020), 723
K. Matveev, “Macdonald-positive specializations of the algebra of symmetric functions: proof of the Kerov conjecture”, Ann. Math., 189:1 (2019), 277–316
A. M. Vershik, “Three Theorems on the Uniqueness of the Plancherel Measure from Different Viewpoints”, Proc. Steklov Inst. Math., 305 (2019), 63–77
P. P. Nikitin, “The absolute of the comb graph”, Teoriya predstavlenii, dinamicheskie sistemy, kombinatornye i algoritmicheskie metody. XXX, Zap. nauchn. sem. POMI, 481, POMI, SPb., 2019, 125–135
Stéphane Laurent, Lecture Notes in Mathematics, 2252, Séminaire de Probabilités L, 2019, 83
A. M. Vershik, A. V. Malyutin, “The Absolute of Finitely Generated Groups: II. The Laplacian and Degenerate Parts”, Funct. Anal. Appl., 52:3 (2018), 163–177
A. M. Vershik, A. V. Malyutin, “The absolute of finitely generated groups: I. Commutative (semi)groups”, Eur. J. Math., 4:4 (2018), 1476–1490
J. Math. Sci. (N. Y.), 240:5 (2019), 539–550
A. M. Vershik, A. V. Malyutin, “Asymptotic behavior of the number of geodesics in the discrete Heisenberg group”, J. Math. Sci. (N. Y.), 240:5 (2019), 525–534
Filip D. Jevtić, Marija Jelić, Rade T. Živaljević, “Cyclohedron and Kantorovich–Rubinstein Polytopes”, Arnold Math J., 4:1 (2018), 87
A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333
A. M. Vershik, P. B. Zatitskii, “Universal adic approximation, invariant measures and scaled entropy”, Izv. Math., 81:4 (2017), 734–770
A. V. Kolesnikov, D. A. Zaev, “Optimal transportation of processes with infinite Kantorovich distance: independence and symmetry”, Kyoto J. Math., 57:2 (2017), 293–324
A. M. Vershik, A. V. Malyutin, “Infinite geodesics in the discrete Heisenberg group”, J. Math. Sci. (N. Y.), 232:2 (2018), 121–128
È. B. Vinberg, S. E. Kuznetsov, “Evgenii (Eugene) Borisovich Dynkin (obituary)”, Russian Math. Surveys, 71:2 (2016), 345–371
A. R. Minabutdinov, “Limiting curves for polynomial adic systems”, J. Math. Sci. (N. Y.), 224:2 (2017), 286–303
Vershik A.M., “Asymptotic theory of path spaces of graded graphs and its applications”, Jap. J. Math., 11:2 (2016), 151–218
Stéphane Laurent, Lecture Notes in Mathematics, 2168, Séminaire de Probabilités XLVIII, 2016, 445
A. M. Vershik, “Equipped graded graphs, projective limits of simplices, and their boundaries”, J. Math. Sci. (N. Y.), 209:6 (2015), 860–873

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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