Related papers: Construction and convergence results for stable we…
We introduce and analyze a discrete-time network process in which each node holds a (weak) preference ordering over a finite set of alternatives and updates by local Borda aggregation. At each step, a node forms a weighted average…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
Several authors have studied convergence in distribution to the Brownian web under diffusive scaling of Markovian random walks. In a paper by R. Roy, K. Saha and A. Sarkar, convergence to the Brownian web is proved for a system of…
The Brownian web (BW) is a collection of coalescing Brownian paths indexed by the plane. It appears in particular as continuous limit of various discrete models of directed forests of coalescing random walks and navigation schemes. Radial…
We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…
We consider the continuous time symmetric random walk with a slow bond on $\mathbb Z$, which rates are equal to $1/2$ for all bonds, except for the bond of vertices $\{-1,0\}$, which associated rate is given by $\alpha n^{-\beta}/2$, where…
We prove new results on lazy random walks on finite graphs. To start, we obtain new estimates on return probabilities $P^t(x,x)$ and the maximum expected hitting time $t_{\rm hit}$, both in terms of the relaxation time. We also prove a…
The Drainage Network is a system of coalescing random walks, exhibiting long-range dependence before coalescence, introduced by Gangopadhyay, Roy, and Sarkar. Coletti, Fontes, and Dias proved its convergence to the Brownian Web under…
We give a short overview on our work on ancestral lineages in spatial population models with local regulation. We explain how an ancestral lineage can be interpreted as a random walk in a dynamic random environment. Defining regeneration…
We consider non-homogeneous random walks on the two-dimensional positive quadrant $\mathbb{N}^2$ and the one-dimensional slab $\{0,1,\dots,k\}\times\mathbb{N}$. In the 1960's the following question was asked for $\mathbb{N}^2$: is it true…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and V\"ollering, 2016] and prove a…
We consider the simple random walk on the infinite cluster of a general class of percolation models on $\mathbb{Z}^d$, $d\geq 3$, including Bernoulli percolation as well as models with strong, algebraically decaying correlations. For almost…
Coalescing simple random walks in the plane form an infinite tree. A natural directed distance on this tree is given by the number of jumps between branches when one is only allowed to move in one direction. The Brownian web distance is the…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…
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 study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A {\bf 293},…
In this paper, we explore the reduction of functionality in a complex system as a consequence of cumulative random damage and imperfect reparation, a phenomenon modeled as a dynamical process on networks. We analyze the global…
We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states which is independent of the order in which the nodes are updated. We…