Related papers: Connectivity patterns in loop percolation I: the r…
We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such…
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' links. In contrast, in agglomerative percolation (AP)…
Most networks of interest do not live in isolation. Instead they form components of larger systems in which multiple networks with distinct topologies coexist and where elements distributed amongst different networks may interact directly.…
Understanding how network structure constrains and enables information processing is a central problem in the statistical mechanics of interacting systems. Here we study random networks across the structural percolation transition and…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
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…
Realistic network-like systems are usually composed of multiple networks with interacting relations such as school-enterprise research and development collaboration networks. Here we study the percolation properties of a special kind of…
Studies of the dynamics of nonlinear recurrent neural networks often assume independent and identically distributed couplings, but large-scale connectomics data indicate that biological neural circuits exhibit markedly different…
Percolation theory characterizing the robustness of a network has applications ranging from biology, to epidemic spreading, and complex infrastructures. Percolation theory, however, only concern the typical response of a infinite network to…
These notes are focused on three recent results in discrete random geometry, namely: the proof by Duminil-Copin and Smirnov that the connective constant of the hexagonal lattice is \sqrt{2+\sqrt 2}; the proof by the author and Manolescu of…
We investigate the problem of percolation of words in a random environment. To each vertex, we independently assign a letter $0$ or $1$ according to Bernoulli r.v.'s with parameter $p$. The environment is the resulting graph obtained from…
We study fundamental characteristics for the connectivity of multi-hop D2D networks. Devices are randomly distributed on street systems and are able to communicate with each other whenever their separation is smaller than some connectivity…
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…
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…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
The k-neighbor graph is a directed percolation model on the hypercubic lattice Z d in which each vertex independently picks exactly k of its 2d nearest neighbors at random, and we open directed edges towards those. We prove that the…
Zhang found a simple, elegant argument deducing the non-existence of an infinite open cluster in certain lattice percolation models (for example, p=1/2 bond percolation on the square lattice) from general results on the uniqueness of an…
We investigate a property that extends the Danos-Regnier correctness criterion for linear logic proof-structures. The property applies to the correctness graphs of a proof-structure: it states that any such graph is acyclic and the number…
Consider an independent site percolation model on $\Z^d,\ d\geq 2$, with parameter $p \in (0,1)$, where there are only nearest neighbor bonds and long range bonds of length $k$ parallel to some coordinate axis. We show that the percolation…
In this chapter of the e-book "Self-Organized Criticality Systems" we summarize some theoretical approaches to self-organized criticality (SOC) phenomena that involve percolation as an essential key ingredient. Scaling arguments, random…