Related papers: Mesoscopics and fluctuations in networks

We consider an ensemble of fully connected networks of N oscillators coupled harmonically with random springs and show, using Random Matrix Theory considerations, that both the average phonon heat current and its variance are…

Mesoscopic effects associated with wave propagation in spacetime with metric stochasticity are studied. We show that the scalar and spinor waves in a stochastic spacetime behave similarly to the electrons in a disordered system. Viewing…

Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…

Uncovering structural properties of ecological networks is a crucial starting point of studying the system's stability in response to various types of perturbations. We analyze pollination and seed disposal networks, which are…

We consider large networks of theta neurons and use the Ott/Antonsen ansatz to derive degree-based mean field equations governing the expected dynamics of the networks. Assuming random connectivity we investigate the effects of varying the…

Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is…

The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…

The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…

The stationary isotropic Poisson line process was used to derive upper bounds on mean excess network geodesic length in Aldous and Kendall [Adv. in Appl. Probab. 40 (2008) 1-21]. The current paper presents a study of the geometry and…

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…

We study the transport properties of an Aharonov-Bohm ring containing two quantum dots. One of the dots has well-separated resonant levels, while the other is chaotic and is treated by random matrix theory. We find that the conductance…

Motivated by recent experiments on large quantum dots, we consider the energy spectrum in a system consisting of $N$ particles distributed among $K<N$ independent sub-systems, such that the energy of each sub-system is a quadratic function…

The occurrence of mesoscopic fluctuations in statistical systems implies, from the point of view of dynamical theory, the existence of local instabilities. However, the presence of such fluctuations can make a system, as a whole, more…

We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…

Networks of strongly-coupled neurons with random connectivity exhibit chaotic, asynchronous fluctuations. In previous work, we showed that when endowed with an additional low-rank connectivity consisting of the outer product of orthogonal…

We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a…

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…

Realistic large-scale networks display an heterogeneous distribution of connectivity weights, that might also randomly vary in time. We show that depending on the level of heterogeneity in the connectivity coefficients, different…

Consider a realization of a Poisson process in R^2 with intensity 1 and take a maximal up/right path from the origin to (N,N) consisting of line segments between the points, where maximal means that it contains as many points as possible.…

Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the…