Related papers: Power laws in zero-range processes on random netwo…
Kauffman net is a dynamical system of logical variables receiving two random inputs and each randomly assigned a boolean function. We show that the attractor and transient lengths exhibit scaleless behavior with power-law distributions over…
We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…
By constructing jointly a random graph and an associated exploration process, we define the dynamics of a "parking process" on a class of uniform random graphs as a measure-valued Markov process, representing the empirical degree…
We consider the one-dimensional partially asymmetric zero range process where the hopping rates as well as the easy direction of hopping are random variables. For this type of disorder there is a condensation phenomena in the thermodynamic…
We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networks using packets moving with two different dynamical rules; random diffusion and locally navigated diffusive motion with preferred edges.…
In discrete contexts such as the degree distribution for a graph, \emph{scale-free} has traditionally been \emph{defined} to be \emph{power-law}. We propose a reasonable interpretation of \emph{scale-free}, namely, invariance under the…
We study the large deviations of the power injected by the active force for an Active Ornstein-Uhlenbeck Particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in…
We study a random walk problem on the hierarchical network which is a scale-free network grown deterministically. The random walk problem is mapped onto a dynamical Ising spin chain system in one dimension with a nonlocal spin update rule,…
We study the effects of random fluctuations on quantum phase transitions by the energy gap analysis. For the infinite-ranged spin-glass models with a transverse field, we find that a strong sample-to-sample fluctuation effect leads to broad…
Distribution functions of relative velocities among particles in a vibrated bed of powder are studied both numerically and theoretically. In the solid phase where granular particles remain near their local stable states, the probability…
We investigate the effect of noise on Random Boolean Networks. Noise is implemented as a probability $p$ that a node does not obey its deterministic update rule. We define two order parameters, the long-time average of the Hamming distance…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
Nature is full of random networks of complex topology describing such apparently disparate systems as biological, economical or informatical ones. Their most characteristic feature is the apparent scale-free character of interconnections…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
We consider a class of scale-free inhomogeneous random graphs, which includes some long-range percolation models. We study the maximum degree in such graphs in a growing observation window and show that its limiting distribution is Frechet.…
Nonequilibrium fluctuations of a tagged, or distinguished particle in a class of one dimensional mean-zero zero-range systems with sublinear, increasing rates are derived. In Jara-Landim-Sethuraman (2009), processes with at least linear…
Random graph models are a recurring tool-of-the-trade for studying network structural properties and benchmarking community detection and other network algorithms. Moreover, they serve as test-bed generators for studying diffusion and…
Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…
A complete understanding of real networks requires us to understand the consequences of the uneven interaction strengths between a system's components. Here we use the minimum spanning tree (MST) to explore the effect of weight assignment…
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…