Related papers: Erratum: Percolation on random Johnson-Mehl tessel…
Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
We consider a stationary face-to-face tessellation $X$ of $\mathbb{R}^d$ and introduce several percolation models by colouring some of the faces black in a consistent way. Our main model is cell percolation, where cells are declared black…
The study published in IJMPD 27(4):1850040, 2018 provided a numerical result for the frequency-shift of GWs due to dispersion in interstellar medium. In order to adjust the metric functions of the originally improperly matched `background'…
The original paper, as published in Nuclear Physics B in 1988, had a few factor-of-two errors. Some people got confused by those errors. The purpose of these errata is to make things clear. The revised version of the complete article is…
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. They confirm most of their results in spite of larger systems…
Correction to The Annals of Statistics (1989) 17 1749--1766 [URL: http://links.jstor.org/sici?sici=0090-5364%28198912%2917%3A4%3C1749%3AEPEFSP%3E 2.0.CO%3B2-9]
For Encyclopedia of Complexity and Systems Science (Springer Verlag). No abstract. I. Definition and Introduction II. Methods III. Quantities and Exponents IV. Fractal Dimension; Incipient Infinite Cluster V. Simple Renormalisation Group…
We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…
We consider two-species random sequential adsorption (RSA) in which species A and B adsorb randomly on a lattice with the restriction that opposite species cannot occupy nearest-neighbor sites. When the probability $x_A$ of choosing an A…
Corrigendum : An inverse problem in corrosion detection:stability estimates, J. Inv. Ill-posed Problems 12 (4) (2004), 349-367.
When considering stochastic integration and the theory of stochastic differential equations, P. Protter's textbook \cite{protter} undoubtedly is a main piece of standard literature. Not only is it well-written, but it also contains various…
This is an erratum to math.AG/9803126, Tohoku 51 (1999) 489-537. This erratum describes: 1. the failure of the algorithm in [AMR] and [Morelli1] for the strong factorization pointed out by Kalle Karu, 2. the statement of a refined weak…
In our paper "Dendroidal sets as models for homotopy operads" (J. Topol. 4 (2011), no. 2, 257-299, and arXiv:0902.1954), we made the wrong claim about the behaviour of the tensor product with respect to cofibrations of dendroidal sets. We…
We study non-random fluctuation in the first passage percolation on $\mathbb{Z}^d$ and show that it diverges for any dimension. We also prove the divergence of the non-random shape fluctuation, which was conjectured in [Yu Zhang. The…
We correct the second main theorem of the previous paper "A perturbation of the Dunkl harmonic oscillator on the line", by the first two authors. The corrections concern mainly certain estimates, which were also improved by adding more…
For first passage percolation on $\mathbb{Z}^2$ with i.i.d. bounded edge weights, we consider the upper tail large deviation event; i.e., the rare situation where the first passage time between two points at distance $n$, is macroscopically…
This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.1.
Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…
In this article, we give a counter-example to Lemma 12 of the article "On Operations and Linear Extensions of Well Partially Ordered Sets" by Maciej Malicki and Aleksander Rutkowski.