Related papers: Ergodic Theory on Stationary Random Graphs
We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the…
We show that the stationary distribution of a finite Markov chain can be expressed as the sum of certain normal distributions. These normal distributions are associated to planar graphs consisting of a straight line with attached loops. The…
In this paper, we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process, which may serve as a mobile wireless network model. The transition probability matrix…
Rank 1 inhomogeneous random graphs are a natural generalization of Erd\H{o}s R\'enyi random graphs. In this generalization each node is given a weight. Then the probability that an edge is present depends on the product of the weights of…
Stationarity is a key assumption in many statistical models for random processes. With recent developments in the field of graph signal processing, the conventional notion of wide-sense stationarity has been extended to random processes…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
A switching random walk, commonly known under the misnomer `oscillating random walk', is a real-valued Markov chain whose distribution of increments is determined by the sign of the current position. We explicitly identify an invariant…
It is demonstrated how to represent asymptotically mean stationary (AMS) random sources with values in standard spaces as mixtures of ergodic AMS sources. This an extension of the well known decomposition of stationary sources which has…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
Graphs have become pervasive tools to represent information and datasets with irregular support. However, in many cases, the underlying graph is either unavailable or naively obtained, calling for more advanced methods to its estimation.…
We study the Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
In this paper, we construct an infinite stationary Diffusion Limited Aggregation (SDLA) on the upper half planar lattice, growing from an infinite line, with local growth rate proportional to the stationary harmonic measure. We prove that…
The stability method is very useful for obtaining exact solutions of many extremal graph problems. Its key step is to establish the stability property which, roughly speaking, states that any two almost optimal graphs of the same order $n$…
In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and…
Using an rotation of Yuan, we observe that the gradient graph of any semiconvex function is a Liouville manifold, that is, does not admit bounded harmonic functions. As a corollary, we find that any entire solution of the fourth order…
This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…
In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
We study dynamical systems forced by a combination of random and deterministic noise and provide criteria, in terms of Lyapunov exponents, for the existence of random attractors with continuous structure in the fibres. For this purpose, we…