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Probabilistic cellular automata. Theory, applications and future perspectives. (English) Zbl 1401.68010
Emergence, Complexity and Computation 27. Cham: Springer (ISBN 978-3-319-65556-7/hbk; 978-3-319-65558-1/ebook). xviii, 344 p. (2018).

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Publisher’s description: This book explores Probabilistic Cellular Automata (PCA) from the perspectives of statistical mechanics, probability theory, computational biology and computer science. PCA are extensions of the well-known Cellular Automata models of complex systems, characterized by random updating rules. Thanks to their probabilistic component, PCA offer flexible computing tools for complex numerical constructions, and realistic simulation tools for phenomena driven by interactions among a large number of neighboring structures. PCA are currently being used in various fields, ranging from pure probability to the social sciences and including a wealth of scientific and technological applications. This situation has produced a highly diversified pool of theoreticians, developers and practitioners whose interaction is highly desirable but can be hampered by differences in jargon and focus. This book – just as the workshop on which it is based – is an attempt to overcome these difference and foster interest among newcomers and interaction between practitioners from different fields. It is not intended as a treatise, but rather as a gentle introduction to the role and relevance of PCA technology, illustrated with a number of applications in probability, statistical mechanics, computer science, the natural sciences and dynamical systems. As such, it will be of interest to students and non-specialists looking to enter the field and to explore its challenges and open issues.
The articles of mathematical interest will be reviewed individually.
Indexed articles:
Fernández, Roberto; Louis, Pierre-Yves; Nardi, Francesca R., Overview: PCA models and issues, 1-30 [Zbl 1402.68127]
Merks, Roeland M. H., Probabilistic cellular automata in the visual arts, 31-34 [Zbl 1402.00034]
Cirillo, Emilio N. M.; Nardi, Francesca R.; Spitoni, Cristian, Basic ideas to approach metastability in probabilistic cellular automata, 37-51 [Zbl 1402.37016]
Dai Pra, Paolo; Sartori, Elena; Tolotti, Marco, Strategic interaction in interacting particle systems, 53-67 [Zbl 1418.91404]
van Enter, Aernout C. D., Scaling and inverse scaling in anisotropic bootstrap percolation, 69-77 [Zbl 1402.37023]
Járai, Antal A., The sandpile cellular automaton, 79-88 [Zbl 1402.37018]
Lancia, Carlo; Scoppola, Benedetto, Ising model on the torus and PCA dynamics: reversibility, irreversibility, and fast tunneling, 89-104 [Zbl 1402.37019]
Louis, Pierre-Yves; Minelli, Ida G., Synchronization in interacting reinforced stochastic processes, 105-118 [Zbl 1402.37064]
Maes, Christian, Nonequilibrium physics aspects of probabilistic cellular automata, 119-128 [Zbl 1402.37020]
Fukś, Henryk, An example of computation of the density of ones in probabilistic cellular automata by direct recursion, 131-144 [Zbl 1402.68128]
Taati, Siamak, Statistical equilibrium in deterministic cellular automata, 145-164 [Zbl 1402.37021]
Gerin, Lucas, Epidemic automaton and the Eden model: various aspects of robustness, 165-178 [Zbl 1402.68129]
Taggi, Lorenzo, Convergence time of probabilistic cellular automata on the torus, 179-196 [Zbl 1402.37022]
Słowiński, Piotr, Percolation operators and related models, 197-214 [Zbl 1402.37065]
Bagnoli, Franco; Rechtman, Raúl, Phase transitions of cellular automata, 215-236 [Zbl 1402.37015]
Fatès, Nazim; Chevrier, Vincent; Bouré, Olivier, A trade-off between simplicity and robustness? Illustration on a lattice-gas model of swarming, 239-259 [Zbl 1402.37017]

MSC:
68-06 Proceedings, conferences, collections, etc. pertaining to computer science
37-06 Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory
37B15 Dynamical aspects of cellular automata
68Q80 Cellular automata (computational aspects)
00B15 Collections of articles of miscellaneous specific interest
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