Reconstruction sequences and equipartition measures: An examination of the asymptotic equipartition property

IEEE Transactions on Information Theory

Volumn 43, Issue 6, 1997, Pages 1935-1947

  Lewis, John T ^a   Pfister, Charles E ^b   Russell, Raymond P ^a   Sullivan, Wayne G ^a,c  

^a DUBLIN INSTITUTE FOR ADVANCED STUDIES   (Ireland)

^b EPFL   (Switzerland)

^c UNIVERSITY COLLEGE DUBLIN   (Ireland)

Author keywords

Asymptotic equipartition property; Empirical measure; Ergodic; Kolmogorov; Large deviations; Reconstruction; Stationary

Indexed keywords

COMPUTER SIMULATION; PROBABILITY; THEOREM PROVING;

ASYMPTOTIC EQUIPARTITION PROPERTY; ERGODIC MEASUREMENT; RECONSTRUCTION SEQUENCES; SHANNON ENTROPY;

INFORMATION THEORY;

EID: 0031276568     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.641557     Document Type: Article

References (16)

1. L. Breiman, "The individual ergodic theorem of information theory," Ann. Math. Statist., vol. 28, pp. 809-811, 1957.
2. I. Csiszár, "Sanov property, generalized I-projection and a conditional limit theorem," Ann. Probab., vol. 12, pp. 768-793, 1984.
3. J. M. van Campenhout and T. M. Cover, "Maximum entropy and conditional probability," IEEE Trans. Inform. Theory, vol. IT-27, pp. 483-89, July 1981.
4. J. W. Gibbs, Elementary Principles of Statistical Mechanics. New Haven, CT: Yale Univ. Press, 1902.
5. A. N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung (Ergebnisse der Math.). Berlin, Germany: Springer, 1933
6. ; translated as Foundations of Probability. New York: Chelsea, 1956.
7. O. E. Lanford, "Entropy and equilibrium states in classical statistical mechanics," in Lecture Notes in Physics, vol. 20. Berlin, Germany: Springer, 1973, pp. 1-113.
8. J. T. Lewis and C.-E. Pfister, "Thermodynamic probability theory: Some aspects of large deviations," Russ. Math. Surv., vol. 50, no. 2, pp. 279-317, 1995.
9. J. T. Lewis, C.-E. Pfister, and W. G. Sullivan, "Large deviations and the thermodynamic formalism: A new proof of the equivalence of ensembles," in On Three Levels, M. Fannes, C. Maes, and A. Verbeure, Eds. New York: Plenum, 1994, pp. 183-193.
10. _, "The equivalence of ensembles for lattice systems: Some examples and a counterexample," J. Stat. Mech., vol. 77, pp. 397-419, 1994.
11. _, "Entropy, concentration of probability and conditional limit theorems," Markov Processes and Related Fields, vol. 1, pp. 319-386, 1995.
12. B. McMillan, "The basic theorems of information theory," Ann. Math. Statist., vol. 24, pp. 196-219, 1953.
13. D. Ruelle, "Correlation functional," J. Math. Phys., vol. 6, pp. 201-220, 1965.
14. C. E. Shannon, "A mathematical theory of communications," Bell Syst. Tech. J., vol. 27, pp. 379-423, pp. 623-656, 1948.
15. P. Shields, "Two divergence-rate counterexamples," J. Theor. Prob., vol. 6, pp. 521-545, 1993.
16. _, "The ergodic theory of discrete sample paths," in Graduate Studies in Mathematics, vol. 13. Providence, RI: Amer. Math. Soc., 1996.