Related papers: Longitudinal Network Models and Permutation-Unifor…
We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$.…
We consider a class of discrete time Markov chains with state space [0,1] and the following dynamics. At each time step, first the direction of the next transition is chosen at random with probability depending on the current location. Then…
We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then, we show that the sample mean of the generator of the exponential family is an…
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…
This paper proposes a family of network centralities called fixed-point centralities. This centrality family is defined via the fixed point of permutation equivariant mappings related to the underlying network. Such a centrality notion is…
We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered…
We derive some key extremal features for $k$th order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a…
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
We study a colored generalization of the famous simple-switch Markov chain for sampling the set of graphs with a fixed degree sequence. Here we consider the space of graphs with colored vertices, in which we fix the degree sequence and…
We study the limit behaviour of a generally non-linear ordinary differential equation whose solution is a superadditive generalisation of a stochastic matrix, and provide necessary and sufficient conditions for this solution to be ergodic,…
Temporal exponential random graph models (TERGM) are powerful statistical models that can be used to infer the temporal pattern of edge formation and elimination in complex networks (e.g., social networks). TERGMs can also be used in a…
We develop a general theory for Markov chains whose transition probabilities are the coefficients of descent operators on combinatorial Hopf algebras. These model the breaking-then-recombining of combinational objects. Examples include the…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…
The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. For many complex systems, however, it is useful to develop continuous-time models of…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
We consider continuous-space, discrete-time Markov chains on $\mathbb{R}^d$, that admit a finite number $N$ of metastable states. Our main motivation for investigating these processes is to analyse random Poincar\'e maps, which describe…
We consider the irreducibility of switch-based Markov chains for the approximate uniform sampling of Hamiltonian cycles in a given undirected dense graph on $n$ vertices. As our main result, we show that every pair of Hamiltonian cycles in…