Related papers: Reply to the comment by Jacobs and Thorpe
Corner percolation is a dependent bond percolation model on Z^2 introduced by B\'alint T\'oth, in which each vertex has exactly two incident edges, perpendicular to each other. G\'abor Pete has proven in 2008 that under the maximal entropy…
It is known that the critical probability for the percolation transition is not a sharp threshold, actually it is a region of non-zero width $\Delta p_c$ for systems of finite size. Here we present evidence that for complex networks $\Delta…
Comment on R. Planet, S. Santucci, J. Ortin, Phys. Rev. Lett. 102, 094502 (2009) about the rescaling of the data and the data collapse. Reply to be found here.
In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree…
This is a comment on recent paper by Rourke et al. titled "Spectroscopic Evidence for Multiple Order Parameters in the Heavy Fermion Superconductor CeCoIn5" (cond-mat/0409562v1 22 Sep 2004). We argue that the features observed by Rourke…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
The immediate purpose of the paper was neither to review the basic definitions of percolation theory nor to rehearse the general physical notions of universality and renormalization (an important technique to be described in Part Two). It…
Reply to a comment by T. Rakovszky, F. Pollmann, and C. W von Keyserlingk [arXiv:2010.07969].
We make comments on the paper by Miller [{\it J. Theor. Biol.} {\bf 234} (2005) 511].
We apply connectedness percolation theory to fractal liquids of hard particles, and make use of a Percus-Yevick liquid state theory combined with a geometric connectivity criterion. We find that in fractal dimensions the percolation…
Reply to ``Comment on [Phys. Rev. Lett. 81, 630 (1998)]''
In this Letter, we show that the explosive percolation is a novel continuous phase transition. The order-parameter-distribution histogram at the percolation threshold is studied in Erd\H{o}s-R\'{e}nyi networks, scale-free networks, and…
The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
In dynamical percolation, the status of every bond is refreshed according to an independent Poisson clock. For graphs which do not percolate at criticality, the dynamical sensitivity of this property was analyzed extensively in the last…
This note establishes a universal directed landscape limit for last passage percolation models in an intermediate scaling regime. We find as a quick consequence the transversal fluctuations for geodesics taken near the axis. We extend the…
We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and…
Rigidity percolation (RP) is the emergence of mechanical stability in networks. Motivated by the experimentally observed fractal nature of materials like colloidal gels and disordered fiber networks, we study RP in a fractal network.…
Recent numerical results on the fractal structure of two-dimensional quantum gravity coupled to $c=-2$ matter are reviewed. Analytic derivation of the fractal dimensions based on the Liouville theory and diffusion equation is also…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…