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A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$…

We introduce a general model of trapping for random walks on graphs. We give the possible scaling limits of these Randomly Trapped Random Walks on $\mathbb {Z}$. These scaling limits include the well-known fractional kinetics process, the…

We find Gaussian cutoff profiles for the total variation distance to stationarity of a random walk on a multiplex network: a finite number of directed configuration models sharing a vertex set, each with its own bounded degree distribution…

This paper proposes an attributed network growth model. Despite the knowledge that individuals use limited resources to form connections to similar others, we lack an understanding of how local and resource-constrained mechanisms explain…

We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold…

Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…

The Brownian web is a random object that occurs as the scaling limit of an infinite system of coalescing random walks. Perturbing this system of random walks by, independently at each point in space-time, resampling the random walk…

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…

In this work, we study the topological transition on the associated networks in a model proposed by Saeedian et al. (Scientific Reports 2019 9:9726), which considers a coupled dynamics of node and link states. Our goal was to better…

We propose a model to create synthetic networks that may also serve as a narrative of a certain kind of infrastructure network evolution. It consists of an initialization phase with the network extending tree-like for minimum cost and a…

We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic…

We study the graph structure of large random dissections of polygons sampled according to Boltzmann weights, which encompasses the case of uniform dissections or uniform $p$-angulations. As their number of vertices $n$ goes to infinity, we…

Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We…

In this paper we construct an object which we call the full Brownian web (FBW) and prove that the collection of all space-time trajectories of a class of one-dimensional stochastic flows converges weakly, under diffusive rescaling, to the…

Barab\'asi-Albert's `Scale Free' model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however,…

We introduce a model of tree-rooted planar maps weighted by their number of $2$-connected blocks. We study its enumerative properties and prove that it undergoes a phase transition. We give the distribution of the size of the largest…

We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…

Local convergence of bounded degree graphs was introduced by Benjamini and Schramm. This result was extended further by Lyons to bounded average degree graphs. In this paper we study the convergence of random tree sequences with given…

The Brownian map is a random geodesic metric space arising as the scaling limit of random planar maps. We strengthen the so-called confluence of geodesics phenomenon observed at the root of the map, and with this, reveal several properties…

Tree-based protocols are ubiquitous in distributed systems. They are flexible, they perform generally well, and, in static conditions, their analysis is mostly simple. Under churn, however, node joins and failures can have complex global…