Gács, P.: Reliable cellular automata with self-organization. J. Stat. Phys. 103, 45–267 (2001)
Article ADS MathSciNet MATH Google Scholar
Toom, A.: Algorithmical unsolvability of the ergodicity problem for binary cellular automata. Markov Process. Relat. F. 6, 569–577 (2000)
MathSciNet MATH Google Scholar
Kurdyumov, G.L.: An algorithm-theoretic method for the study of homogeneous random networks. Lect. Notes Math. 6, 471–504 (1980)
Malyshev, V.A.: Quantum grammars. J. Math. Phys. 41, 4508–4520 (2000)
Article ADS MathSciNet MATH Google Scholar
Toom, A.: Non-ergodicity in a 1-d particle process with variable length. J. Stat. Phys. 115, 895–924 (2004)
Article ADS MathSciNet MATH Google Scholar
Maes, C.: New trends in interacting particle systems. Markov Process. Relat. F. 11, 283–288 (2005)
MathSciNet MATH Google Scholar
Gohlke, P., Spindeler, T.: Ergodic frequency measures for random substitutions. Stud. Math. 255, 265–301 (2020)
Article MathSciNet MATH Google Scholar
Li, W.: Generating non-trivial long range correlations and \(1/f\) spectra by replication and mutation. Int. J. Bifurc. Chaos. 2(1), 137–154 (1992)
Article ADS MATH Google Scholar
Lindenmayer, A.: Mathematical models for cellular interaction in development, parts I and II. J. Theor. Biol. 18, 280–315 (1968)
Article ADS MATH Google Scholar
Salgado-García, R., Ugalde, E.: Exact scaling in the expansion-modification system. J. Stat. Phys. 153, 842–863 (2013)
Article ADS MathSciNet MATH Google Scholar
Toom, A., Ramos, A. D., Rocha, A. V., Simas, A. B.: Random processes with variable length.\(28^0\) Colóquio Brasileiro de Matemática, Impa Monographs, (2011)
Gohlke, P., Mitchell, A., Rust, D., Samuel, T.: Measure theoretic entropy of random substitution subshifts. Ann. Henri Poincaré 24, 277–323 (2023)
Article ADS MathSciNet MATH Google Scholar
Karpelevich, F. I., Malyshev, V. A., Petrov, A. I., Pirogov, S. A., Rybko, A. N.: Context free evolution of words. Collection Seminaires Inria. Vol. 4413, (2002)
Harris, T.E.: Contact interactions on a lattice. Ann. Probab. 2(6), 969–988 (1974)
Article MathSciNet MATH Google Scholar
Toom, A.: A family of uniform nets of formal neurons. Soviet Math. Dokl. 183, 49 (1968)
Costa, L.T., Ramos, A.D.: Totally asymmetric coalescence process. Markov Process. Relat. F. 29, 67–97 (2023)
MathSciNet MATH Google Scholar
Toom, A., Vasilyev, N., Stavskaya, O., Mityushin, L., Kurdyumov, G., Pirogov, S.: Stochastic cellular systems: ergodicity, memory, morphogenesis. Ed. by R. Dobrushin, V, Kryukov and A. Toom. Nonlinear Science: theory and applications. Manchester University Press, (1990)
Rocha, A.V., Simas, A.B., Toom, A.: Substitution operators. J. Stat. Phys. 143, 585–618 (2011)
Article ADS MathSciNet MATH Google Scholar
Athreya, K.B., Vidyashankar, A.N.: Branching processes. Springer-Verlag, Berlin (1972)
Edwards, R.E.: Functional analysis: theory and applications. Dover Publications Inc, New York (1995)
Toom, A.: Every continuous operator has an invariant measure. J. Stat. Phys. 129, 555–566 (2007)
Article ADS MathSciNet MATH Google Scholar
Depoorter, J., Maes, C.: Stavskaya’s measure is weakly Gibbsian. Markov Process. Related Fields 12, 791–804 (2006)
MathSciNet MATH Google Scholar
Gács, P.: Probabilistic cellular automata with Andrei Toom. Braz. J. Prob. Stat. 38, 285–301 (2024)
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