A reader's guide to Gacs's "positive rates" paper

Journal of Statistical Physics

Volumn 103, Issue 1-2, 2001, Pages 1-44

  Gray, Lawrence F ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Cellular automaton; Error correction; Phase transition; Self simulation; Stability; Universal computation

Indexed keywords

EID: 0035532619     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004824203467     Document Type: Article

References (9)

1. J. van den Berg and H. Kesten, Inequalities with applications to percolation and reliability, J. Appl. Probab. 22:556-569 (1985).
2. P. Gacs, Reliable computation with cellular automata. J. Comput. Syst. Sci. 32:15-78 (1986).
3. P. Gacs, G. Kurdyumov, and L. Levin, One-dimensional homogeneous media dissolving finite islands, Problems of Information Transmission 14:92-96 (1978).
4. L. Gray, The positive rates problem for attractive nearest-neighbor systems on ℤ, Z. Wahrsch. verw. Gebiete 61:389-404 (1982).
5. L. Gray, The behavior of processes with statistical mechanical properties, Percolation Theory and Ergodic Theory of Infinite Particle Systems (Springer-Verlag, New York, 1987). pp. 131-167.
6. G. Kurdyumov, An example of a nonergodic homogeneous one-dimensional random medium with positive transition probabilities. Sov. Math. Dokl. 19:211-214 (1978).
7. T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985).
8. K. Park, Ergodicity and mixing rate of one-dimensional cellular automata, Ph.D. Thesis (Boston University, Boston, 1996).
9. A. Toom, Stable and attrative trajectories in multicomponent systems, Advances in Probability, Vol. 6 (Dekker, New York, 1980). pp. 549-575.