Related papers: Directed Percolation Criticality in Eternal Inflat…
We investigate both analytically and numerically the ensemble of minimum-weight loops and paths in the negative-weight percolation model on random graphs with fixed connectivity and bimodal weight distribution. This allows us to study the…
The idea of biased symmetries to avoid or alleviate cosmological problems caused by the appearance of some topological defects is familiar in the context of domain walls, where the defect statistics lend themselves naturally to a…
In BP models with hundreds of fluxes, we compute the effects of cosmological dynamics on the probability distribution of landscape vacua. Starting from generic initial conditions, we find that most fluxes are dynamically driven into a…
We study the behavior of the random walk on the infinite cluster of independent long range percolation in dimensions $d=1,2$, where $x$ and $y$ a re connected with probability $\sim\beta/\|x-y\|^{-s}$. We show that when $d<s<2d$ the walk is…
The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…
An anthropic understanding of the cosmological constant requires that the vacuum energy at late time scans from one patch of the universe to another. If the vacuum energy during inflation also scans, the various patches of the universe…
As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical Erd\H{o}s-R\'enyi…
Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…
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 the cosmological dynamics associated with volume weighted measures of eternal inflation, in the Bousso-Polchinski model of the string theory landscape. We find that this measure predicts that observers are most likely to find…
In a situation like eternal inflation, where our data is replicated at infinitely-many other space-time events, it is necessary to make a prior assumption about our location to extract predictions. The principle of mediocrity entails that…
Models of percolation processes on networks currently assume locally tree-like structures at low densities, and are derived exactly only in the thermodynamic limit. Finite size effects and the presence of short loops in real systems however…
The static properties of the fundamental model for epidemics of diseases allowing immunity (susceptible-infected-removed model) are known to be derivable by an exact mapping to bond percolation. Yet when performing numerical simulations of…
Connectivity and reachability on temporal networks, which can describe the spreading of a disease, decimation of information or the accessibility of a public transport system over time, have been among the main contemporary areas of study…
We numerically generate the six-dimensional landscape of D3-brane inflation and identify patches of eternal inflation near sufficiently flat inflection points of the potential. We show that reasonable measures that select patches of eternal…
Chain Inflation is an alternative to slow roll inflation in which the universe undergoes a series of transitions between different vacua. The density perturbations (studied in this paper) are seeded by the probabilistic nature of tunneling…
We discuss aspects of the problem of assigning probabilities in eternal inflation. In particular, we investigate a recent suggestion that the lowest energy de Sitter vacuum in the landscape is effectively stable. The associated proposal for…
This is a comprehensive report on the phase transition between two turbulent states of electroconvection in nematic liquid crystals, which was recently found by the authors to be in the directed percolation (DP) universality class [K. A.…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We…