Related papers: Contact process with simultaneous spatial and temp…
We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with…
We study the Susceptible-Infected-Recovered model in complex networks, considering that not all individuals in the population interact in the same way between them. This heterogeneity between contacts is modeled by a continuous disorder. In…
We study the contact process on a random bipartite connection hypergraph generated from two Poisson point processes, with mark-dependent connection thresholds. For asymmetric infection rates and asymmetric power law tail decays of the two…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
We study the delocalisation transition which takes places in one-dimensional disordered systems when the random potential exhibits specific long-range correlations. We consider the case of weak disorder; using a systematic perturbative…
We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very…
We study the dynamics of an interface (active domain) between different absorbing regions in models with two absorbing states in one dimension; probabilistic cellular automata models and interacting monomer-dimer models. These models…
The behavior at criticality of spatial SIR (susceptible/infected/recovered) epidemic models in dimensions two and three is investigated. In these models, finite populations of size N are situated at the vertices of the integer lattice, and…
We introduce a model for directed percolation with a long-range temporal diffusion, while the spatial diffusion is kept short ranged. In an interpretation of directed percolation as an epidemic process, this non-Markovian modification can…
We study a model of two-dimensional interacting monomers which has two symmetric absorbing states and exhibits two kinds of phase transition; one is an order-disorder transition and the other is an absorbing phase transition. Our focus is…
Physical contact or proximity is often a necessary condition for the spread of infectious diseases. Common destinations, typically referred to as hubs or points of interest, are arguably the most effective spots for the type of disease…
Jamming transition is traditionally regarded as a geometric transition governed by static contact networks. Recently, dynamic phase transitions of athermal particles under periodic shearing provide a new lens on this problem, leading to a…
Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary…
Dynamical systems running on the top of complex networks has been extensively investigated for decades. But this topic still remains among the most relevant issues in complex network theory due to its range of applicability. The contact…
Traditional epidemic models consider that individual processes occur at constant rates. That is, an infected individual has a constant probability per unit time of recovering from infection after contagion. This assumption certainly fails…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
According to recent numerical results from lattice models, the critical exponents of systems with many absorbing states and an order parameter coupled to a non-diffusive conserved field coincide with those of the linear interface depinning…
In real social networks, person-to-person interactions are known to be heterogeneous, which can affect the way a disease spreads through a population, reaches a tipping point in the fraction of infected individuals, and becomes an epidemic.…
By incorporating segregated spatial domain and individual-based linkage into the SIS (susceptible-infected-susceptible) model, we investigate the coupled effects of random walk and intragroup interaction on contagion. Compared with the…
Diseases and other contagion phenomena in nature and society can interact asymmetrically, such that one can benefit from the other, which in turn impairs the first, in analogy with predator-prey systems. Here, we consider two models for…