Related papers: Directed percolation and directed animals
We consider a directed random walk on the backbone of the infinite cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the ``ancestral lineage'' of an individual in the stationary…
Probabilistic cellular automata are prototypes of non equilibrium critical phenomena. This class of models includes among others the directed percolation problem (Domany Kinzel model) and the dynamical Ising model. The critical properties…
Contents: A. Introduction B. High Temperature Expansions for the Ising Model C. Characteristic Functions and Cumulants D. The One Dimensional Chain E. Directed Paths and the Transfer Matrix F. Moments of the Correlation Function G. The…
We study self-similarity in one-dimensional probabilistic cellular automata (PCA) using the renormalization technique. We introduce a general framework for algebraic construction of renormalization groups (RG) on cellular automata and apply…
We introduce a model for directed percolation with a long-range temporal diffusion, while the spatial diffusion is kept short ranged. In an interpretation of directed percolation as an epidemic process, this non-Markovian modification can…
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.…
The probability distributions of the order parameter for two models in the directed percolation universality class were evaluated. Monte Carlo simulations have been performed for the one-dimensional generalized contact process and the…
A model of directed percolation processes with colors and flavors that is equivalent to a population model with many species near their extinction thresholds is presented. We use renormalized field theory and demonstrate that all…
The self-similar cluster fluctuations of directed bond percolation at the percolation threshold are studied using techniques borrowed from inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical simulations based on the…
Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically…
A directed percolation process with two symmetric particle species exhibiting exclusion in one dimension is investigated numerically. It is shown that if the species are coupled by branching ($A\to AB$, $B\to BA$) a continuous phase…
We consider directed percolation with an absorbing boundary in 1+1 and 2+1 dimensions. The distribution of cluster lifetimes and sizes depend on the boundary. The new scaling exponents can be related to the exponents characterizing standard…
Percolation clusters are probably the simplest example for scale--invariant structures which either are governed by isotropic scaling--laws (``self--similarity'') or --- as in the case of directed percolation --- may display anisotropic…
The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…
In this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension. In particular we determine numerically the order parameter, its fluctuations as well as the susceptibility as a function…
Spatial L{\'{e}}vy-like flights are introduced as a way in the absorbing phase transitions to produce non-local interactions. We utilize the autoencoder, an unsupervised learning method, to predict the critical points for $(1+1)$-d directed…
We discuss a model for directed percolation in which the flux of material along each bond is a dynamical variable. The model includes a physically significant limiting case where the total flux of material is conserved. We show that the…
False-vacuum eternal inflation can be described as a random walk on the network of vacua of the string landscape. In this paper we show that the problem can be mapped naturally to a problem of directed percolation. The mapping relies on two…
We study a probabilistic cellular automaton to describe two population biology problems: the threshold of species coexistence in a predator-prey system and the spreading of an epidemic in a population. By carrying out time-dependent…
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the mean field limit, stochastic order, duality, and the relation…