Related papers: Edge-averaging dynamics on finite graphs: moment d…
In several settings (e.g., sensor networks and social networks), nodes of a graph are equipped with initial opinions, and the goal is to estimate the average of these opinions using local operations. A natural algorithm to achieve this is…
We analyze the asynchronous version of the DeGroot dynamics: In a connected graph $G$ with $n$ nodes, each node has an initial opinion in $[0,1]$ and an independent Poisson clock. When a clock at a node $v$ rings, the opinion at $v$ is…
We consider the averaging process on an infinite connected graph with bounded degree and independent, identically distributed starting values or initial opinions. Assuming that the law of the initial opinion of a vertex has a finite second…
In the voter model, each node of a graph has an opinion, and in every round each node chooses independently a random neighbour and adopts its opinion. We are interested in the consensus time, which is the first point in time where all nodes…
We analyze the following dynamics on a connected graph $(V,E)$ with $n$ vertices. Let $V = I \bigcup B$, where the set of interior vertices $I \ne \emptyset$ is disjoint from the set of boundary vertices $B \neq \emptyset$. Given $p > 1$…
Sourav Chatterjee, Persi Diaconis, Allan Sly and Lingfu Zhang, prompted by a question of Ramis Movassagh, renewed the study of a process proposed in the early 1980s by Jean Bourgain. A state vector $v \in \mathbb R^n$, labeled with the…
Let $G = (V,E)$ be a connected directed graph on $n$ vertices. Assign values from the set $\{1,2,\dots,n\}$ to the vertices of $G$ and update the values according to the following rule: uniformly at random choose a vertex and update its…
We introduce a dynamic random hypergraph model constructed from a bipartite graph. In this model, both vertex sets of the bipartite graph are generated by marked Poisson point processes. Vertices of both vertex sets are equipped with marks…
The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of…
We consider two simple asynchronous opinion dynamics on arbitrary graphs where every node $u$ has an initial value $\xi_u(0)$. In the first process, the NodeModel, at each time step $t\ge 0$, a random node $u$ and a random sample of $k$ of…
Statistical inference on graphs is a burgeoning field in the applied and theoretical statistics communities, as well as throughout the wider world of science, engineering, business, etc. In many applications, we are faced with the reality…
We consider the following dynamics on a connected graph $(V,E)$ with $n$ vertices. Given $p>1$ and an initial opinion profile $f_0:V \to [0,1]$, at each integer step $t \ge 1$ a uniformly random vertex $v=v_t$ is selected, and the opinion…
Theoretical computer science plays an important role in the understanding of social networks and their properties. We can model information rippling throughout social networks, or the opinions of social media users for example, using graph…
Consider the following iterated process on a hypergraph $H$. Each vertex $v$ has an initial vertex weight. At each step, we uniformly at random select an edge $F$ in $H$, and for each vertex $v$ in $F$ we replace the weight of $v$ by the…
Temporal graphs (in which edges are active at specified times) are of particular relevance for spreading processes on graphs, e.g.~the spread of disease or dissemination of information. Motivated by real-world applications, modification of…
We consider the averaging process on a graph, that is the evolution of a mass distribution undergoing repeated averages along the edges of the graph at the arrival times of independent Poisson processes. We establish cutoff phenomena for…
In majority dynamics, agents located at the vertices of an undirected simple graph update their binary opinions synchronously by adopting those of the majority of their neighbors. On infinite unimodular transitive graphs (e.g., Cayley…
We consider the two-opinion voter model on a regular random graph with n vertices and degree $d \geq 3$. It is known that consensus is reached on time scale n and that on this time scale the volume of the set of vertices with one opinion…
Let $G$ be a connected edge-weighted graph of order $n$ and size $m$. Let $w:E(G)\rightarrow \mathbb{R}^{\geq 0}$ be the weighting function. We assume that $w$ is normalised, that is, $\sum_{e\in E(G)} w(e)=m$. The weighted distance…
The edge flipping is a non-reversible Markov chain on a given connected graph, which is defined by Chung and Graham in [CG12]. In the same paper, its eigenvalues and stationary distributions for some classes of graphs are identified. We…