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We discuss attacks and infections at propagating fronts of percolation processes based on the extended general epidemic process. The scaling behavior of the number of the attacked and infected sites in the long time limit at the ordinary and tricritical percolation transitions is governed by specific composite operators of the field-theoretic representation of this process. We calculate corresponding critical exponents for tricritical percolation in mean-field theory and for ordinary percolation to 1-loop order. Our results agree well with the available numerical data.
We study a hierarchy of directed percolation (DP) processes for particle species A, B, ..., unidirectionally coupled via the reactions A -> B, ... When the DP critical points at all levels coincide, multicritical behavior emerges, with density expone
We review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous non-equilibrium active to absorbing state phase transitions whose asymptotic features
The recent work by Achlioptas, DSouza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bond occupation. Despite the active research on this subject, several ques
These lectures provide an introduction to the directed percolation and directed animals problems, from a physicists point of view. The probabilistic cellular automaton formulation of directed percolation is introduced. The planar duality of the diode
A model named `Colored Percolation has been introduced with its infinite number