Related papers: Universality classes of generalized epidemic proce…
We consider TASEP in continuous time with non-random initial conditions and arbitrary fixed density of particles rho. We show GOE Tracy-Widom universality of the one-point fluctuations of the associated height function. The result phrased…
Regression models applied to network data where node attributes are the dependent variables poses a methodological challenge. As has been well studied, naive regression neither properly accounts for community structure, nor does it account…
We study explosive percolation (EP) on Erd\"{o}s-R\'{e}nyi network for product rule (PR) and sum rule (SR). Initially, it was claimed that EP describes discontinuous phase transition, now it is well-accepted as a probabilistic model for…
The spread of an epidemic process is considered in the context of a spatial SIR stochastic model that includes a parameter $0\le p\le 1$ that assigns weights $p$ and $1- p$ to global and local infective contacts respectively. The model was…
The emergence of large-scale connectivity and synchronization are crucial to the structure, function and failure of many complex socio-technical networks. Thus, there is great interest in analyzing phase transitions to large-scale…
We consider the adjacency matrix of the ensemble of Erd\H{o}s-R\'enyi random graphs which consists of graphs on $N$ vertices in which each edge occurs independently with probability $p$. We prove that in the regime $pN \gg 1$ these matrices…
We introduce an exponential random graph model for networks with a fixed degree distribution and with a tunable degree-degree correlation. We then investigate the nature of a percolation transition in the correlated network with the Poisson…
These notes are based on a talk given at the 2018 Arizona School of Analysis and Mathematical Physics. We give a comprehensive introduction to the KPZ universality class, a conjectured class of stochastic process with local interactions…
We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The…
We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a…
Avalanches in mean-field models can be mapped to memoryless branching processes defining a universality class. We present a reduced expression mapping a broad family of critical and subcriticial avalanches in mean-field models at the…
Given a graph $G$, we consider a model for a random cover of $G$ by taking two parallel copies of $G$ and crossing every pair of parallel edges randomly with probability $q$ independently of each other. The resulting graph $G_q$, is a…
Particle hopping is a common feature in heterogeneous media. We explore such motion by using the widely applicable formalism of the continuous time random walk and focus on the statistics of rare events. Numerous experiments have shown that…
Understanding how internal community structure shapes the course of epidemics remains a fundamental challenge in modeling real-world populations. Standard metapopulation models often assume uniform mixing within communities, overlooking how…
We consider single-particle quantum transport on parametrized complex networks. Based on general arguments regarding the spectrum of the corresponding Hamiltonian, we derive bounds for a measure of the global transport efficiency defined by…
The contact process and the slightly different susceptible-infected-susceptible model are studied on long-range connected networks in the presence of random transition rates by means of a strong disorder renormalization group method and…
We consider a general criterion to discern the nature of the threshold in epidemic models on scale-free (SF) networks. Comparing the epidemic lifespan of the nodes with largest degrees with the infection time between them, we propose a…
We study the dynamics of epidemic spreading processes aimed at spontaneous dissemination of information updates in populations with complex connectivity patterns. The influence of the topological structure of the network in these processes…
In co-infections, positive feedback between multiple diseases can accelerate outbreaks. In a recent letter Chen, Ghanbarnejad, Cai, and Grassberger (CGCG) introduced a spatially homogeneous mean-field model system for such co-infections,…
By generating transient encounters between individuals beyond their immediate social environment, transport can have a profound impact on the spreading of an epidemic. In this work, we consider epidemic dynamics in the presence of the…