4.2k citations · 9.8k across the 134 of their papers we have counts for
61 papers · 1 filter
Strongly-connected percolation on directed lattices
M. E. J. Newman, P. Grassberger, R. M. Ziff
We study percolation on lattices with directed bonds, focusing on the behavior of strongly-connected percolation clusters -- clusters in which every site is reachable from every ot…
Aftermath Epidemics: Percolation on the Sites Visited by Generalized Random Walks
Mohadeseh Feshanjerdi, Amir Ali Masoudi, Peter Grassberger +1
We study percolation on the sites of a finite lattice visited by a generalized random walk of finite length with periodic boundary conditions. More precisely, consider Levy flights…
Many universality classes in an interface model restricted to non-negative heights
Peter Grassberger, Deepak Dhar, P. K. Mohanty
We present a simple one dimensional stochastic model with three control parameters and a surprisingly rich zoo of phase transitions. At each (discrete) site and time , an in…
Kardar-Parisi-Zhang type dynamics with periodic tilt dependence of the propagation velocity in 1+1 dimensions
Peter Grassberger
We consider the evolution of interfaces with a diffusive term and a generalized Kardar-Parisi-Zhang (KPZ) non-linearity, which results in a propagation velocity that depends period…
Revisiting a Low-Dimensional Model with Short Range Interactions and Mean Field Critical Behavior
Peter Grassberger
In all local low-dimensional models, scaling at critical points deviates from mean field behavior -- with one possible exception. This exceptional model with ``ordinary" behavior i…
Morphological transitions in supercritical generalized percolation and moving interfaces in media with frozen randomness
Peter Grassberger
We consider the growth of clusters in disordered media at zero temperature, as exemplified by supercritical generalized percolation and by the random field Ising model. We show tha…
Comment on "Inferring Statistical Complexity"
Peter Grassberger
Nearly 30 years ago, J.P. Crutchfield and K. Young proposed in Phys. Rev. Lett. {\bf 63}, 105 (1989) some supposedly novel measures of time series complexity, and their relations t…
Self-trapping self-repelling random walks
Peter Grassberger
Although the title seems self-contradictory, it does not contain a misprint. The model we study is a seemingly minor modification of the "true self-avoiding walk" (TSAW) model of A…
How fast does a random walk cover a torus?
Peter Grassberger
We present high statistics simulation data for the average time that a random walk needs to cover completely a 2-dimensional torus of size $L\time…
Universality and Asymptotic Scaling in Drilling Percolation
Peter Grassberger
We present simulations of a 3-d percolation model studied recently by K.J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016)], obtained with a new and more efficient algorithm. T…
Critical phenomena on k-booklets
Peter Grassberger
We define a `k-booklet' to be a set of k semi-infinite planes with and , glued together at the edges (the `spine') y=0. On such booklets we study t…
The Oslo model, hyperuniformity, and the quenched Edwards-Wilkinson model
Peter Grassberger, Deepak Dhar, P. K. Mohanty
We present simulations of the 1-dimensional Oslo rice pile model in which the critical height at each site is randomly reset after each toppling. We use the fact that the stationar…
Recent advances and open challenges in percolation
N. A. M. Araújo, P. Grassberger, B. Kahng +2
Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related…
On the Continuum Time Limit of Reaction-Diffusion Systems
Peter Grassberger
The parity conserving branching-annihilating random walk (pc-BARW) model is a reaction-diffusion system on a lattice where particles can branch into offsprings with even an…
Two-dimensional SIR epidemics with long range infection
Peter Grassberger
We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in…
SIR epidemics with long range infection in one dimension
Peter Grassberger
We study epidemic processes with immunization on very large 1-dimensional lattices, where at least some of the infections are non-local, with rates decaying as power laws p(x) ~ x^…
Information theoretic aspects of the two-dimensional Ising model
Hon Wai Lau, Peter Grassberger
We present numerical results for various information theoretic properties of the square lattice Ising model. First, using a bond propagation algorithm, we find the difference $2H_L…
Agglomerative Percolation on Bipartite Networks: A Novel Type of Spontaneous Symmetry Breaking
Hon Wai Lau, Maya Paczuski, Peter Grassberger
Ordinary bond percolation (OP) can be viewed as a process where clusters grow by joining them pairwise, by adding links chosen randomly one by one from a set of predefined `virtual…
Corrections to Scaling for Watersheds, Optimal Path Cracks, and Bridge Lines
E. Fehr, K. J. Schrenk, N. A. M. Araújo +4
We study the corrections to scaling for the mass of the watershed, the bridge line, and the optimal path crack in two and three dimensions. We disclose that these models have numer…
Random Sequential Renormalization and Agglomerative Percolation in Networks: Application to Erd"os-R'enyi and Scale-free Graphs
Golnoosh Bizhani, Peter Grassberger, Maya Paczuski
We study the statistical behavior under random sequential renormalization(RSR) of several network models including Erd"os R'enyi (ER) graphs, scale-free networks and an annealed mo…
Agglomerative Percolation in Two Dimensions
Claire Christensen, Golnoosh Bizhani, Seung-Woo Son +2
We study a process termed "agglomerative percolation" (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their nei…
Random Sequential Renormalization of Networks I: Application to Critical Trees
Golnoosh Bizhani, Vishal Sood, Maya Paczuski +1
We introduce the concept of Random Sequential Renormalization (RSR) for arbitrary networks. RSR is a graph renormalization procedure that locally aggregates nodes to produce a coar…
Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles
David V. Foster, Jacob G. Foster, Maya Paczuski +1
Ensembles of networks are used as null models in many applications. However, simple null models often show much less clustering than their real-world counterparts. In this paper, w…
Local persistence in directed percolation
Peter Grassberger
We reconsider the problem of local persistence in directed site percolation. We present improved estimates of the persistence exponent in all dimensions from 1+1 to 7+1, obtained b…