Related papers: Random interlacements for vertex-reinforced jump p…
We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection…
Graph processes exhibit a temporal structure determined by the sequence index and and a spatial structure determined by the graph support. To learn from graph processes, an information processing architecture must then be able to exploit…
This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on…
We present an explicit connected spanning structure that appears in a random graph just above the connectivity threshold with high probability.
Random walks on graphs can be slow. To speed them up, imagine that at each step instead of choosing the neighbor at random, there is a small probability $\varepsilon>0$ that we can choose it. We show that in this case, at least for graphs…
Connected automated driving has the potential to significantly improve urban traffic efficiency, e.g., by alleviating issues due to occlusion. Cooperative behavior planning can be employed to jointly optimize the motion of multiple…
A Random Walk in Changing Environment (RWCE) is a weighted random walk on a locally finite, connected graph $G$ with random, time-dependent edge-weights. This includes self-interacting random walks, where the edge-weights depend on the…
We study the relaxation time in the random walk with jumps. The random walk with jumps combines random walk based sampling with uniform node sampling and improves the performance of network analysis and learning tasks. We derive various…
We prove an upper bound for the $\varepsilon$-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to $\mathsf{T}_{\mathsf{RW}(G)}\ln(|V|/\varepsilon)$, where |V|…
We study some properties of the random interlacement model on a transient weighted graph, which was introduced by A. Teixeira in ["Interlacement percolation on transient weighted graphs", Augusto Teixeira, Electronic Journal of Probability…
Let $K_{s,t}^{(r)}$ denote the $r$-uniform hypergraph obtained from the graph $K_{s,t}$ by inserting $r-2$ new vertices inside each edge of $K_{s,t}$. We prove essentially tight bounds on the size of a largest $K_{s,t}^{(r)}$-subgraph of…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
In a coalescing random walk, a set of particles make independent random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues the random walk through the graph.…
We consider an edge-weighted uniform random graph with a given degree sequence (Repeated Configuration Model) which is a useful approximation for many real-world networks. It has been observed that the vertices which are separated from the…
Jumping poses a significant challenge for quadruped robots, despite being crucial for many operational scenarios. While optimisation methods exist for controlling such motions, they are often time-consuming and demand extensive knowledge of…
We prove an explicit formula of hitting times in terms of enumerations of spanning trees for random walks on general connected graphs. We apply the formula to improve Lawler's bound of hitting times for general graphs, prove a sharp bound…
Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…
We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are…
Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random…
An induced forest of a graph G is an acyclic induced subgraph of G. The present paper is devoted to the analysis of a simple randomised algorithm that grows an induced forest in a regular graph. The expected size of the forest it outputs…