|
Matrices of polynomials, positivity, and finite equivalence of Markov chains
Author(s):
Brian
Marcus;
Selim
Tuncel
Journal:
J. Amer. Math. Soc.
6
(1993),
131-147.
MSC:
Primary 28D20;
Secondary 15A48, 60J10
MathSciNet review:
1168959
Retrieve article in:
PDF
This article is available free of charge
References |
Similar articles |
Additional information
References:
-
- [AM]
- R. Adler and B. Marcus, Topological entropy and equivalence of dynamical systems, Mem. Amer. Math. Soc., vol. 219, Amer. Math. Soc., Providence, RI, 1979. MR 533691 (83h:28027)
- [Ash]
- J. Ashley, Bounded-to-one factors of an aperiodic shift of finite type are
 -to- almost everywhere factors also, Ergodic Theory Dynamical Systems 10 (1990), 615-625. MR 1091417 (92d:58055) - [AMPT]
- J. Ashley, B. Marcus, D. Perrin, and S. Tuncel, Surjective extensions of sliding block codes, SIAM J. Discrete Math. (to appear). MR 1241398 (95h:68145)
- [D]
- V. De Angelis, Ph. D. thesis, Univ. of Washington, Seattle, 1992.
- [H1]
- D. Handelman, Positive polynomials and product type actions of compact groups, Mem. Amer. Math. Soc., vol. 320, Amer. Math. Soc., Providence, RI, 1985. MR 783217 (86h:46091)
- [H2]
- -, Positive polynomials, convex integral polytopes, and a random walk problem, Lecture Notes in Math., vol. 1282, Springer-Verlag, Berlin, Heidelberg, and New York, 1987. MR 914972 (89b:06014)
- [H3]
- -, Eventual positivity and finite equivalence for matrices of polynomials, preprint.
- [HLP]
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge, 1959.
- [K]
- B. Kitchens, Linear algebra and subshifts of finite type, Contemp. Math., vol. 26, Amer. Math. Soc., Providence, RI, 1981, pp. 231-248. MR 737405 (85m:28022)
- [KT1]
- B. Kitchens and S. Tuncel, Finitary measures for subshifts of finite type and sofic systems, Mem. Amer. Math. Soc., vol. 338, Amer. Math. Soc., Providence, RI, 1985. MR 818917 (87h:58110)
- [KT2]
- -, On measures induced on subsystems, Lecture Notes in Math., vol. 1342, Springer-Verlag, Berlin, Heidelberg, and New York, 1988, pp. 455-464. MR 970570 (89m:28031)
- [Kr]
- W. Krieger, On the finitary isomorphisms of Markov shifts that have finite expected coding time, Z. Wahr. 65 (1983), 323-328. MR 722135 (85e:28034)
- [MT]
- B. Marcus and S. Tuncel, The weight-per-symbol polytope and scaffolds of invariants associated with Markov chains, Ergodic Theory Dynamical Systems 11 (1991), 129-180 MR 1101088 (92g:28038)
- [P1]
- W. Parry, A finitary classification of topological Markov chains and sofic systems, Bull. London Math. Soc. 9 (1977), 86-92. MR 0482707 (58:2763)
- [P2]
- -, Problems and perspectives in the theory of Markov shifts, Lecture Notes in Math., vol. 1342, Springer-Verlag, Berlin, Heidelberg, and New York, 1988, pp. 626-637. MR 970575 (89m:28033)
- [PS]
- W. Parry and K. Schmidt, Natural coefficients and invariants for Markov shifts, Invent. Math. 76 (1984), 15-32. MR 739621 (86b:28022a)
- [PT]
- W. Parry and S. Tuncel, On the classification of Markov chains by finite equivalence, Ergodic Theory Dynamical Systems 1 (1981), 303-335. MR 662472 (83j:28020)
- [Poin]
- H. Poincaré, Sur les équations algébriques, C. R. Acad. Sci. Paris 8 (1883), 1418.
- [Se]
- E. Seneta, Non-negative matrices and Markov chains, Springer-Verlag, Berlin, Heidelberg, and New York, 1981. MR 2209438
- [T]
- S. Tuncel, Conditional pressure and coding, Israel J. Math. 39 (1981), 101-112. MR 617293 (82j:28012)
Similar Articles:
Retrieve articles in Journal of the American Mathematical Society
with
MSC:
28D20,
15A48, 60J10
Retrieve articles in all Journals with
MSC:
28D20,
15A48, 60J10
Additional Information:
DOI:
10.1090/S0894-0347-1993-1168959-X
PII:
S0894-0347-1993-1168959-X
Copyright of article:
Copyright
1993,
American Mathematical Society
|
