Related papers: Mean-Field and Anomalous Behavior on a Small-World…
A Markov chain (MC) formalism is used to investigate the mean-square displacement (MSD) of a random walker on Newman-Watts (NW) networks. It leads to a precise analysis of the conditions for the emergence of anomalous sub- or…
We point out how geometric features affect the scaling properties of non-equilibrium dynamic processes, by a model for surface growth where particles can deposit and evaporate only in dimer form, but dissociate on the surface. Pinning…
Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for…
We consider quantum and classical first-order transitions, at equilibrium and under out-of-equilibrium conditions, mainly focusing on quench and slow quasi-adiabatic protocols. For these phenomena, we review the finite-size scaling theory…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…
Oscillator networks with an asymmetric bipolar distribution of natural frequencies are useful representations of power grids. We propose a mean-field model that captures the onset, form and linear stability of frequency synchronization in…
We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying…
Models for cross-sectional network data have become increasingly well-developed in recent decades, and are widely used. This has led to a growing interest in the connection between such cross-sectional models and the behavioral processes…
Many real-world phenomena can be modelled as dynamical processes on networks, a prominent example being the spread of infectious diseases such as COVID-19. Mean-field approximations are a widely used tool to analyse such dynamical processes…
The objective of statistical physics is to understand macroscopic behavior of a many-body system from the interactions of the constituents of that system. When many-body systems reach critical states, simple universal and scaling behaviors…
We investigate finite size scaling aspects of disorder reaction-diffusion processes in one dimension utilizing both numerical and analytical approaches. The former averages the spectrum gap of the associated evolution operators by doubling…
It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To…
A general algorithm is presented for estimating the nonlinear instability threshold, $\sigma_c$, for subcritical transitions in systems where the linearized dynamics is significantly non-normal (i.e. subcritical bifurcations of {\em…
Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behaviour between an ordered, large-world and a disordered, small-world behaviour. Using the ergodic Pachner flips…
Consider the class of Ensemble Square Root filtering algorithms for the numerical approximation of the posterior distribution of nonlinear Markovian signals partially observed with linear observations corrupted with independent measurement…
We study the off equilibrium dynamics of a mean field disordered systems which can be interpreted both as a long range interaction spin glass and as a particle in a random potential. The statics of this problem is well known and exhibits a…
The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…
We consider a stochastic sandpile where the sand-grains of unstable sites are randomly distributed to the nearest neighbors. Increasing the value of the threshold condition the stochastic character of the distribution is lost and a…
The decay timescales of the quasinormal modes of a massive scalar field have an intriguing behavior: they either grow or decay with increasing angular harmonic numbers $\ell$, depending on whether the mass of the scalar field is small or…
We present high-accuracy quasi-stationary (QS) simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs. The critical behavior is analyzed in the framework of the…