Related papers: Directed Percolation Criticality in Eternal Inflat…
We propose a new measure for eternal inflation, based on search optimization and first-passage statistics. This work builds on the dynamical selection mechanism for vacua based on search optimization proposed recently by the author and…
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…
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…
In Chain Inflation the universe tunnels along a series of false vacua of ever-decreasing energy. The main goal of this paper is to embed Chain Inflation in high energy fundamental physics. We begin by illustrating a simple effective…
We consider the statistical properties of vacua and inflationary trajectories associated with a random multifield potential. Our underlying motivation is the string landscape, but our calculations apply to general potentials. Using random…
We model the essential features of eternal inflation on the landscape of a dense discretuum of vacua by the potential $V(\phi)=V_{0}+\delta V(\phi)$, where $|\delta V(\phi)|\ll V_{0}$ is random. We find that the diffusion of the…
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.…
In a previous paper, two of the authors presented a "regulated" picture of eternal inflation. This picture both suggested and drew support from a conjectured discontinuity in the amplitude for tunneling from positive to negative vacuum…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
We attempt an estimate for the distribution of the tensor mode fraction $r$ over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no…
Chain inflation takes place in the string theory landscape as the universe tunnels rapidly through a series of ever lower energy vacua such as may be characterized by quantized changes in four form fluxes. The string landscape may be well…
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…
We study some aspects of fine tuning in inflationary scenarios within string theory flux compactifications and, in particular, in models of accidental inflation. We investigate the possibility that the apparent fine-tuning of the low energy…
Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a pre-critical to the…
We study oriented percolation on random causal triangulations, those are random planar graphs obtained roughly speaking by adding horizontal connections between vertices of an infinite tree. When the underlying tree is a geometric…
We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…