31 citations · 113 across the 17 of their papers we have counts for
20 papers
Positive-rate PCA and IPS with stationary Bernoulli measures are rapidly forgetful
Irène Marcovici, Siamak Taati
We prove that every probabilistic cellular automaton with strictly positive transition probabilities that admits a stationary Bernoulli measure is exponentially ergodic. Moreover,…
Quasicrystalline Gibbs states in 4-dimensional lattice-gas models with finite-range interactions
Jacek Miȩkisz, Siamak Taati
We construct a four-dimensional lattice-gas model with finite-range interactions that has non-periodic, "quasicrystalline" Gibbs states at low temperatures. Such Gibbs states are p…
Cellular automata, percolation and dynamical dichotomies
Sebastián Barbieri, Felipe García-Ramos, Siamak Taati
We establish a connection between percolation on the Cayley graphs of a group and the dynamical diversity of cellular automata on that group. Specifically, we demonstrate that Gilm…
Zero-one laws for events with positional symmetries
Yahya Ayach, Anthony Khairallah, Tia Manoukian +3
We use an information-theoretic argument due to O'Connell (2000) to prove that every sufficiently symmetric event concerning a countably infinite family of independent and identica…
Characterisation of the Set of Ground States of Uniformly Chaotic Finite-Range Lattice Models
Léo Gayral, Léopoldine Gayral, Mathieu Sablik +1
Chaotic dependence on temperature refers to the phenomenon of divergence of Gibbs measures as the temperature approaches a certain value. Models with chaotic behaviour near zero te…
Reversible cellular automata in presence of noise rapidly forget everything
Siamak Taati
We consider reversible and surjective cellular automata perturbed with noise. We show that, in the presence of positive additive noise, the cellular automaton forgets all the infor…
Self-stabilisation of cellular automata on tilings
Nazim Fatès, Irène Marcovici, Siamak Taati
Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and uniform algorithm) that self-stabilises on the configurations that satisfy these constraint…
Gibbsian representations of continuous specifications: the theorems of Kozlov and Sullivan revisited
Sebastián Barbieri, Ricardo Gómez, Brian Marcus +2
The theorems of Kozlov and Sullivan characterize Gibbs measures as measures with positive continuous specifications. More precisely, Kozlov showed that every positive continuous sp…
Crossover times in bipartite networks with activity constraints and time-varying switching rates
Sem Borst, Frank den Hollander, Francesca Nardi +1
In this paper we study the performance of a bipartite network in which customers arrive at the nodes of the network, but not all nodes are able to serve their customers at all time…
Equivalence of relative Gibbs and relative equilibrium measures for actions of countable amenable groups
Sebastián Barbieri, Ricardo Gómez, Brian Marcus +1
We formulate and prove a very general relative version of the Dobrushin-Lanford-Ruelle theorem which gives conditions on constraints of configuration spaces over a finite alphabet…
Ergodicity of some classes of cellular automata subject to noise
Irène Marcovici, Mathieu Sablik, Siamak Taati
Cellular automata (CA) are dynamical systems on symbolic configurations on the lattice. They are also used as models of massively parallel computers. As dynamical systems, one woul…
Metastability of hard-core dynamics on bipartite graphs
Frank den Hollander, Francesca R. Nardi, Siamak Taati
We study the metastable behaviour of a stochastic system of particles with hard-core interactions in a high-density regime. Particles sit on the vertices of a bipartite graph. New…
Two-dimensional traffic rules and the density classification problem
Nazim Fatès, Irène Marcovici, Siamak Taati
The density classification problem is the computational problem of finding the majority in a given array of votes in a distributed fashion. It is known that no cellular automaton r…
Post-surjectivity and balancedness of cellular automata over groups
Silvio Capobianco, Jarkko Kari, Siamak Taati
We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of…
Statistical equilibrium in deterministic cellular automata
Siamak Taati
Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves to…
Restricted density classification in one dimension
Siamak Taati
The density classification task is to determine which of the symbols appearing in an array has the majority. A cellular automaton solving this task is required to converge to a uni…
Statistical Mechanics of Surjective Cellular Automata
Jarkko Kari, Siamak Taati
Reversible cellular automata are seen as microscopic physical models, and their states of macroscopic equilibrium are described using invariant probability measures. We establish a…
Potts model with invisible colours: Random-cluster representation and Pirogov-Sinai analysis
Aernout C. D. van Enter, Giulio Iacobelli, Siamak Taati
We study a variant of the ferromagnetic Potts model, recently introduced by Tamura, Tanaka and Kawashima, consisting of a ferromagnetic interaction among "visible" colours alon…
First-order transition in Potts models with "invisible' states: Rigorous proofs
Aernout C. D. van Enter, Giulio Iacobelli, Siamak Taati
In some recent papers by Tamura, Tanaka and Kawashima [arXiv:1102.5475, arXiv:1012.4254], a class of Potts models with "invisible" states was introduced, for which the authors argu…
Graph Coloring and Function Simulation
Amir Daneshgar, Ali Reza Rahimi, Siamak Taati
We prove that every partial function with finite domain and range can be effectively simulated through sequential colorings of graphs. Namely, we show that given a finite set $S=\{…