Related papers: Percolation representations of additive particle s…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
We consider a class of multi-type particle systems having similar structure to the contact process and show that additivity is equivalent to the existence of a dual process, extending a result of Harris. We give two additional…
A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened…
Light-matter interaction processes are significantly affected by surrounding electromagnetic environment. Dielectric materials are usually introduced into an interaction picture via their classical properties, e.g. permittivity, appearing…
The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are…
Some examples of translation invariant site percolation processes on the $\Z^2$ lattice are constructed, the most far-reaching example being one that satisfies uniform finite energy (meaning that the probability that a site is open given…
We study an interacting particle system in which moving particles activate dormant particles linked by the components of critical bond percolation. Addressing a conjecture from Beckman, Dinan, Durrett, Huo, and Junge for a continuous…
This chapter is devoted to the analysis of jamming and percolation behavior of two-dimensional systems of elongated particles. We consider both continuous and discrete spaces (with the special attention to the square lattice), as well the…
In this paper we provide an extension of the model discussed in [arXiv:1504.08283] describing two singularly interacting particles on the half-line. In this model, the particles are interacting only whenever at least one particle is…
Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary…
We investigate the entanglement for a model of a particle moving in the lattice (many-body system). The interaction between the particle and the lattice is modelled using Hooke's law. The Feynman path integral approach is applied to compute…
In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for…
High-density (HD) percolation describes the percolation over specific $\kappa$ -clusters, which are the compact sets of sites each connected to $\kappa$ nearest filled sites at least. It takes place in the classical patterns of…
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
The coherent state path integral formulation of certain many particle systems allows for their non perturbative study by the techniques of lattice field theory. In this paper we exploit this strategy by simulating the explicit example of…
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…
We study the emergence of a giant component in a spatial network where the distribution of the metric distances between the nodes is scale-invariant, and the interaction between the nodes has a long-range power-law behavior. The nodes are…
A model for the study of the effective quasistatic conductivity and permittivity of dispersed systems with particle-host interphase, within which many-particle polarization and correlation contributions are effectively incorporated, is…
Consider a system of interacting particles indexed by the nodes of a graph whose vertices are equipped with marks representing parameters of the model such as the environment or initial data. Each particle takes values in a countable state…
Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified…