Local persistence in the directed percolation universality class

@article{Fuchs2008LocalPI,
  title={Local persistence in the directed percolation universality class},
  author={J. Fuchs and J{\"o}rg Schelter and Francesco Ginelli and Haye Hinrichsen},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2008},
  volume={2008},
  pages={04015}
}
We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean field limit. Moreover, we examine a graded persistence probability that a site does not flip more than m times and demonstrate how local persistence can be studied in seed simulations. Finally, the problem of spatial (as opposed to temporal) persistence is… 
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16 Citations
Background Citations
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16 Citations

Local persistence in directed percolation
TLDR
Improved estimates of the exponent of persistence in all dimensions from 1+1 to 7+1 are presented, obtained using new algorithms and using improved implementations of existing ones, and it is shown that scaling is much better satisfied for very large and very small dimensions.
NEWS AND PERSPECTIVES: Efficient numerical study of local persistence in directed percolation
This commentary discusses a recently introduced numerical method developed by Grassberger (2009 J. Stat. Mech. P08021) which allows one to study local persistence in high-dimensional directed…
Scaling of local persistence in the disordered contact process.
TLDR
A nonuniversal algebraic decay of the average persistence for d=1 and enhanced power laws for d>1 is obtained and the equivalence of the persistence with a return probability is proved, a valuable tool for the argumentations.
Universality of the local persistence exponent for models in the directed Ising class in one dimension.
TLDR
This work investigates local persistence in five different models and their variants in the directed Ising (DI) universality class in one dimension and finds that the local persistence exponent in all these models is unity or very close to it.
Novel transition to fully absorbing state without long-range spatial order in directed percolation class
Persistence as the order parameter in a generalized pair-contact process with diffusion
The question of the universality class of the pair-contact process with diffusion (PCPD) is revisited with an alternative approach. We study persistence in a generalized pair-contact process with…
Dynamic phase transition in the contact process with spatial disorder: Griffiths phase and complex persistence exponents.
TLDR
A model which displays the Griffiths phase, i.e., algebraic decay of density with continuously varying exponents in the absorbing phase, with logarithmic periodic oscillations in persistence is presented.
Persistence discontinuity in disordered contact processes with long-range interactions
We study the local persistence probability during non-stationary time evolutions in disordered contact processes with long-range interactions by a combination of the strong-disorder renormalization…
Persistence and first-passage properties in nonequilibrium systems
In this review, we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such…
Dynamic phase transition from localized to spatiotemporal chaos in coupled circle map with feedback.
TLDR
It is observed that persistence could work as a good order parameter for transitions from fully or partially arrested phase, and an explanation of gaps in eigenvalue spectrum of the Jacobian of localized state is given.
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