Related papers: Phase Transitions in the Edge/Concurrent Vertex Mo…
Graph processes that unfold in continuous time are of obvious theoretical and practical interest. Particularly useful are those whose long-term behavior converges to a graph distribution of known form. Here, we review some of the conditions…
The mobility edge, as a central concept in disordered models for localization-delocalization transitions, has rarely been discussed in the context of random matrix theory (RMT). Here we report a new class of random matrix model by direct…
In this work, we revisited the ZGB model in order to study the behavior of its phase diagram when two well-known random networks play the role of the catalytic surfaces: the Random Geometric Graph and the Erd\"{o}s-R\'{e}nyi network. The…
Considering one-dimensional nonminimally-coupled lattice gauge theories, a class of nonlocal one-dimensional systems is presented, which exhibits a phase transition. It is shown that the transition has a latent heat, and, therefore, is a…
Random graphs undergo structural phase transitions that are crucial for dynamical processes and cooperative behavior of models defined on graphs. In this work we investigate the impact of a first-order structural transition on the…
We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with…
It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture…
Conventionally used exponential random graphs cannot directly model weighted networks as the underlying probability space consists of simple graphs only. Since many substantively important networks are weighted, this limitation is…
Exponential family random graph models (ERGMs) can be understood in terms of a set of structural biases that act on an underlying reference distribution. This distribution determines many aspects of the behavior and interpretation of the…
We introduce a new class of latent process models for dynamic relational network data with the goal of detecting time-dependent structure. Network data are often observed over time, and static network models for such data may fail to…
We show existence of a non-trivial phase transition for the contact process, a simple model for infection without immunity, on a network which reacts dynamically to the infection trying to prevent an epidemic. This network initially has the…
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…
Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through…
Consider the complete graph \(K_n\) on \(n\) vertices where each edge \(e\) is independently open with probability \(p_n(e)\) or closed otherwise. Here \(\frac{C-\alpha_n}{n} \leq p_n(e) \leq \frac{C+\alpha_n}{n}\) where \(C > 0\) is a…
This is a status report on a companion subject to extremal combinatorics, obtained by replacing extremality properties with emergent structure, `phases'. We discuss phases, and phase transitions, in large graphs and large permutations,…
First order phase transitions occur discretely from one state to another, however they often display continuous behavior. To understand this nature, it is essential to probe how the emergent phase nucleates, interacts and evolves with the…
We study the appearance of first-order dynamical phase transitions (DPTs) as `intermittent' co-existing phases in the fluctuations of random walks on graphs. We show that the diverging time scale leading to critical behaviour is the waiting…
We investigate the possibility of a striped inhomoegenous phase occurring as an electronic system with an order parameter linearly coupled to the elastic degrees of freedom is tuned through the electronic phase transition. We find that in…
Random graphs, where the connections between nodes are considered random variables, have wide applicability in the social sciences. Exponential-family Random Graph Models (ERGM) have shown themselves to be a useful class of models for…
Random graphs with latent geometric structure are popular models of social and biological networks, with applications ranging from network user profiling to circuit design. These graphs are also of purely theoretical interest within…