Related papers: Directed Percolation Criticality in Eternal Inflat…
Following Freivogel {\it et al} we consider inflation in a predictive (or `friendly') region of the landscape of string vacua, as modeled by Arkani-Hamed, Dimopoulos and Kachru. In such a region the dimensionful coefficients of…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
We compute the distribution of minima that are reached dynamically on multi-field axionic landscapes, both numerically and analytically. Such landscapes are well suited for inflationary model building due to the presence of shift symmetries…
We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability…
Recently, the number of non-standard percolation models has proliferated. In all these models, there exists a phase transition at which long range connectivity is established, if local connectedness increases through a threshold $p_c$. In…
We prove non-universality results for first-passage percolation on the configuration model with i.i.d. degrees having infinite variance. We focus on the weight of the optimal path between two uniform vertices. Depending on the properties of…
We investigate a model of epidemic spreading with partial immunization which is controlled by two probabilities, namely, for first infections, $p_0$, and reinfections, $p$. When the two probabilities are equal, the model reduces to directed…
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…
A striking feature of our universe is its near criticality. The cosmological constant and weak hierarchy problems, as well as the metastability of the electroweak vacuum, can all be understood as problems of criticality. This suggests a…
We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability. We focus on the case when the time interval between subsequent…
We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the…
Universal behavior is a typical emergent feature of critical systems. A paramount model of the non-equilibrium critical behavior is the directed bond percolation process that exhibits an active- to-absorbing state phase transition in the…
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential…
We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously…
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
This Letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd\"{o}s and R\'{e}nyi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two…
We propose an approach to calculate the critical percolation threshold for finite-sized Erdos-Renyi digraphs using minimal Hamiltonian cycles. We obtain an analytically exact result, valid non-asymptotically for all graph sizes, which…
Directed percolation is one of the most prominent universality classes of nonequilibrium phase transitions and can be found in a large variety of models. Despite its theoretical success, no experiment is known which clearly reproduces the…