Related papers: The probability distribution of the average relati…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
One calls attention to the fact that the stochastic physical systems are not random completely. They have both random and regular components of their evolution. Dynamic system is considered to be a special case of physical system with…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or…
The fixed-point analysis refers to the study of fixed-points that arise in the context of complex systems with many interacting entities. In this expository paper, we describe four levels of fixed-points in mean-field interacting particle…
This paper characterises dynamic linkages arising from shocks with heterogeneous degrees of persistence. Using frequency domain techniques, we introduce measures that identify smoothly varying links of a transitory and persistent nature.…
Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and…
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition…
A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approach is offered that effectively propagates the statistics in time. Loss of sensitivity to an…
The variation of the velocity of a periodic signal and its frequency along the world line of a standard emitter (at rest with an observer) are considered in a space with affine connections and metrics. It is shown that the frequency of the…
Structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically.…
In studying randomized search heuristics, a frequent quantity of interest is the first time a (real-valued) stochastic process obtains (or passes) a certain value. The processes under investigation commonly show a bias towards this goal,…
We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
As the amount of linked data published on the web grows, attempts are being made to describe and measure it. However even basic statistics about a graph, such as its size, are difficult to express in a uniform and predictable way. In order…
In this paper, the leading term of the asymptotics of the number of possible final positions of a random walk on a directed Hamiltonian metric graph is found. Consideration of such dynamical systems could be motivated by problems of…
The propagation of an interacting particle pair in a disordered chain is characterized by a set of localization lengths which we define. The localization lengths are computed by a new decimation algorithm and provide a more comprehensive…
We study the motion of a substance in a channel that is part of a network. The channel has 3 arms and consists of nodes of the network and edges that connect the nodes and form ways for motion of the substance. Stationary regime of the flow…
The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…
The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…