Related papers: Coupling from the past for exponentially ergodic o…
We prove a.e. convergence of continuous-time quadratic averages with respect to two commuting $\mathbb{R}$-actions, coming from a single jointly measurable measure-preserving $\mathbb{R}^2$-action on a probability space. The key ingredient…
In this paper a new form of duality for probabilistic cellular automata (PCA) is introduced. Using this duality, an ergodicity result for processes having a dual is proved. Also, conditions on the probabilities defining the evolution of the…
We prove exponential decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first time exponential decay of correlations is proved for continuous-time dynamics…
This paper considers a class of probabilistic cellular automata undergoing a phase transition with an absorbing state. Denoting by ${\mathcal{U}}(x)$ the neighbourhood of site $x$, the transition probability is $T(\eta_x = 1 |…
We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation…
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…
For non-uniform cellular automata (NUCA) with finite memory over an arbitrary universe with multiple local transition rules, we show that pointwise nilpotency, pointwise periodicity, and pointwise eventual periodicity properties are…
We introduce a new class of probabilistic cellular automata that are capable of exhibiting rich dynamics such as synchronization and ergodicity and can be easily inferred from data. The system is a finite-state locally interacting Markov…
We study phase transitions in a long-range one-dimensional cellular automaton with two symmetric absorbing states. It includes and extends several other models, like the Ising and Domany-Kinzel ones. It is characterized by a competing…
In this work, the one-dimensional Cellular Automaton is extended to one that involves two sets of symbols and two global rules. As a main result, the Extended Curtis-Hedlund-Lyndon Theorem is demonstrated. Such constructions can be useful…
In this paper, we investigate some ergodic properties of $Z^{2}$-actions $T_{p,n}$ generated by an additive cellular automata and shift acting on the space of all doubly -infinitive sequences taking values in $Z_{m}$.
We show that for every ergodic and aperiodic probability preserving transformation and $\alpha\in (0,2)$ there exists a function whose associated time series is in the standard domain of attraction of a non-degenerate symmetric…
Reversible Probabilistic Cellular Automata are a special class of automata whose stationary behavior is described by Gibbs-like measures. For those models the dynamics can be trapped for a very long time in states which are very different…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
An introduction to the Propp-Wilson method of coupling-from-the-past for the Ising model is presented. It enables one to obtain exact samples from the equilibrium spin distribution for ferromagnetic interactions. Both uniform and random…
The phase diagram of the coupled sine circle map lattice exhibits a variety of interesting phenomena including spreading regions with spatiotemporal intermittency, non-spreading regions with spatial intermittency, and coherent structures…
We describe a new general connection between $\Lambda$-coalescents and genealogies of continuous-state branching processes. This connection is based on the construction of an explicit coupling using a particle representation inspired by the…
Correlated time series are time series that, by virtue of the underlying process to which they refer, are expected to influence each other strongly. We introduce a novel approach to handle such time series, one that models their interaction…
This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability,…
Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by monte-carlo simulation near a critical point which marks a second-order phase transition from a active state to a effectively unique absorbing state.…