Andrei Toom's articles in English: Mathematics.



1. A. Toom. The Complexity of a Scheme of Functional Elements Realizing the Multiplication of Integers. Soviet Mathematics - Doklady, 1963, v. 3, pp 714-716.
Originally published in Russian


2. A. Toom. A Family of Uniform Nets of Formal Neurons. Soviet Mathematics - Doklady, 1968, v.9, n.6, pp.1338-1341. Originally published in Russian

3. A. Toom. Non-Ergodic Multidimensional Systems of Automata. Problems of Information Transmission.
1974, v. 10, n. 3, pp. 239-246. Originally published in Russian,


4. A. Toom. Monotonic Binary Cellular Automata. Problems of Information Transmission
1976, v. 12, n.1, pp. 33-37. Originally published in Russian.


5. L. Mityushin and A. Toom. Two Results regarding Non-Computability for Univariate Cellular Automata.
Problems of Information Transmission, 1976, v. 12, n.2, pp.135-140. Originally published in Russian.


6. A. Toom. Unstable Multicomponent Systems. Problems of Information Transmission 1976, v. 12, n.3, pp. 220-224.
Originally published in Russian.


7. A. Toom. Monotonic Evolutions in Real Spaces. Lecture Notes in Mathematics, Springer, 1978, v. 653, pp. 1-14.
Originally published in Russian.


8. A. Toom. Stable and Attractive Trajectories in Multicomponent Systems. Multicomponent Random Systems,
Dekker, 1980, v. 6, pp.549-576. Originally published in Russian.


9. A. Toom. Stability in Lattice Systems with Local Prohibitions. Sel. Math. Sov., 1985, v. 4, n. 1, pp. 73-92.
Originally published in Russian.


10. Discrete Local Markov Systems. A survey written by several authors and published in the series
Nonlinear Science: theory and applications, Manchester University Press, 1990.


11. A. Toom. On Critical Phenomena in Interacting Growth Systems. Part I: General.
Journal of Stat. Physics, 1994, v. 74, n. 1/2, pp. 91-109.


12. A. Toom. On Critical Phenomena in Interacting Growth Systems. Part II: Bounded Growth.
Journal of Stat. Physics, 1994, v. 74, n. 1/2, pp. 111-130.


13. A. Toom. Cellular Automata with Errors: Problems for Students of Probability.
Topics in Contemporary Probability and its Applications. CRC Press, 1995.


14. A. Toom. Simple 1-Dimensional Systems with Super-Exponential Relaxation Time.
Journal of Stat. Physics, v. 80, n. 3/4, 1995, pp. 545-563.


15. A. Toom. Tails in Harnesses. Abstract presented to AMS in 1996.

16. A. Toom. Tails in Harnesses. Journal of Stat. Physics, v. 88, n. 1/2, 1997, pp. 347-364.

17. A. Toom. On Periodic Processes of Percolation Cellular Automata. Resenhas de IME/USP, 1998, v. 3, n. 3, pp. 351-357.

18. A. Toom. Pseudo-pinning in a growth model. Markov Processes and Related Fields, 1998, v. 4, n. 4, pp. 663-668.

19. A. Toom. On Percolatoon with Fibers or Layers. Journal of Stat. Physics., v. 96, nn. 1/2, 1999, pp. 429-437.

20. A. Toom. Algoritmic unsolvability of the ergodicity problem for locally interacting processes with contimuous time.
Journal of Stat. Phys., v. 98, nn. 1/2, 2000, pp. 495-501.


21. A. Toom. Algoritmic unsolvability of the ergodicity problem for binary cellular automata.
Markov Processes and Related Fields, v. 6, n. 4, 2000, pp. 569-577.


22. Ilya Piatetsky-Shapiro, Olga Stavskaya and Andrei Toom. Certain Homogeneous Neuron Nets.
Selected Works of Ilya Piatetski-Shapiro. AMS Press, 2000, pp. 277-281.


23. A. Toom. Featured review of Gacs and Gray's articles. Published in Mathematical Reviews in 2002.

24. A. Toom. Contours, convex sets and Cellular Automata. English version. 23-th Brazilian Math Colloquium, IMPA, 2001.

25. A. Toom. On Critical Values for Some Random Processes with Local Interaction in R^2.
In and Out of Equilibrium: Probability with a Physical Flavor. Birkhauser, 2002, pp. 309-319.


26. A. Toom. On large isolated regions in supercritical percolation. Journal of Stat. Physics, v. 109, nn. 5/6, 2002, pp. 1091-1108.

27. A. Toom. Particle systems with variable length. Bulletin of Brasilian Math Society, v. 33, n. 3, Nov 2002, pp. 419-425.

28. Roberto Fernández and Andre Toom.
Non-Gibbsianness of the invariant measures of non-reversible cellular automata with totally asymmetric noise.
Asterisque, v. 287, December 2003, pp. 71-87.


29. A. Toom. Non-ergodicity in a 1-D particle process with variable length.
Journal of Stat. Physics, vol. 115, 2004, nn. 3/4, pp. 895-924.


30. Moisés Lima de Menezes and Andre Toom. A non-linear eroder in presence of one-sided noise.
Brazilian Journal of Probability and Statistics, vol. 20, n. 1, june 2006, pp. 1-12.


31. A. Toom. Every continuous operator has an invariant measure. Journal of Stat. Physics, vol. 129, 2007, n. 3, pp. 555-566.

32. A. D. Ramos and A. Toom. An error correction. Letter to the editor.
Journal of Stat. Physics, vol. 131, n. 1, april 2008, pp. 167-168.


33. Pedro Ferreira de Lima and Andre Toom. Dualities useful in bond percolation.
CUBO, vol. 10, n. 3, october 2008, pp. 93-102.


34. A. D. Ramos and A. Toom. Chaos and Monte-Carlo approximations of the Flip-Annihilation process.
Journal of Stat. Physics, vol. 133, n. 4 (2008), pp. 761-771.


35. A. Toom. Law of Large Numbers for Non-Local Functions on Probabilistic Cellular Automata.
Journal of Stat. Physics, vol. 133, n. 5 (2008), pp. 883-897.


36. A. Toom. Ilia Piatetski-Shapiro in 1963-1973: Passion for Applied Mathematics. . You can also find it here.

37. A. D. Ramos and A. Toom. Nonergodicity and growth are compatible for 1-D local interaction.
Brazilian Journal of Probability and Statistics, vol 24, n. 2 (2010), pp. 400-412.


38. A. D. Ramos and A. Toom. Trajectories in Random Monads.
Journal of Stat. Physics, vol. 142 (2011), n. 1, pp. 201-219. DOI: 10.1007/s10955-010-0087-5


39. A. Rocha, A. Simas, A. Toom. Substitution Operators. Journal of Stat. Physics, vol. 143 (2011), n. 3, pp. 585-618.
DOI: 10.1007/s10955-011-0192-0

40.
A. Toom, A. Ramos, A. Rocha, A. Simas. Random Processes with Variable Length.
28-o Colóquio Brasileiro de Matemática. IMPA, 2011.