Related papers: Large Fluctuations in Stochastically Perturbed Non…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
We study the role of fluctuations in percolation of sparse complex networks. To this end we consider two random correlated realizations of the initial damage of the nodes and we evaluate the fraction of nodes that are expected to remain in…
Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is "statistics of statistics" with two largely separated time scales, offers a consistent…
Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…
We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the…
The long time dynamics of large particles trapped in two inhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of…
Networked dynamical systems, i.e., systems of dynamical units coupled via nontrivial interaction topologies, constitute models of broad classes of complex systems, ranging from gene regulatory and metabolic circuits in our cells to…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
We discuss research done in two important areas of nonequilibrium statistical mechanics: fluctuation dissipation relations and dynamical fluctuations. In equilibrium systems the fluctuation-dissipation theorem gives a simple relation…
It is becoming more and more clear that complex networks present remarkable large fluctuations. These fluctuations may manifest differently according to the given model. In this paper we re-consider hidden variable models which turn out to…
In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
We study analytically giant fluctuations and temporal intermittency in a stochastic one-dimensional model with diffusion and aggregation of masses in the bulk, along with influx of single particles and outflux of aggregates at the…
A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…
Understanding the physics of non-equilibrium systems remains as one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the…
These notes are a written version of lectures given in the 2024 Les Houches Summer School on {\it Large deviations and applications}. They are are based on a series of works published over the last 25 years on steady properties of…
Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or 'noise', is predominantly generated by interactions of the system…