Related papers: Clarification of the Bootstrap Percolation Paradox
Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transition in a driven lattice gas with nearest-neighbor exclusion on a square lattice. A slight extension of the microscopic dynamics with…
There are some papers which describe the use of bootstrap techniques in point process statistics. The aim of the present paper is to show that the form in which bootstrap is used there is dubious. In case of variance estimation of pair…
The Hamming torus of dimension $d$ is the graph with vertices $\{1,\dots,n\}^d$ and an edge between any two vertices that differ in a single coordinate. Bootstrap percolation with threshold $\theta$ starts with a random set of open…
In this paper we describe two bootstrap methods for massive data sets. Naive applications of common resampling methodology are often impractical for massive data sets due to computational burden and due to complex patterns of inhomogeneity.…
Spatial self-similarity is a hallmark of critical phenomena. We study the dynamic process of percolation, in which bonds are incrementally added to an initially empty lattice until the system becomes fully occupied. By tracking the gap --…
In order to investigate the dependence on lattice size of several observables in percolation, the Hoshen-Kopelman algorithm was modified so that growing lattices could be simulated. By this way, when simulating a lattice of size L, lattices…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
The effect of rotational constraint on the properties of lattice models like the self-avoiding walk, lattice animals and percolation is discussed. The results obtained so far, using a variety of exact and approximate techniques, are…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
We investigate via Monte Carlo simulations the kinetically constrained Kob-Andersen lattice glass model showing that, contrary to current expectations, the relaxation process and the dynamical heterogeneities seems to be characterized by…
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility,…
We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes. We present sharp results on the size of the minimum percolating sets and the maximal non-percolating sets. Additional…
We numerically study bootstrap percolation on Kleinberg's spatial networks, in which the probability density function of a node to have a long-range link at distance $r$ scales as $P(r)\sim r^{\alpha}$. Setting the ratio of the size of the…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
In the realm of contemporary physics, the bootstrap method is typically associated with an optimization-based approach to problem-solving. This method leverages our understanding of a specific physical problem, which is used as the…
The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of…
The following article deals with the critical value p_c of the three-dimensional bootstrap percolation. We will check the behavior of p_c for different lengths of the lattice and additionally we will scale p_c in the limit of an infinite…
We introduce and solve a model of hardcore particles on a one dimensional periodic lattice which undergoes an active-absorbing state phase transition at finite density. In this model an occupied site is defined to be active if its left…