Related papers: Interacting vertex reinforced random walks on comp…

Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…

We consider the random walk attachment graph introduced by Saram\"{a}ki and Kaski and proposed as a mechanism to explain how behaviour similar to preferential attachment may appear requiring only local knowledge. We show that if the length…

We continue the investigation of the localization phenomenon for a Vertex Reinforced Random Walk on the integer lattice. We provide some partial results towards a full characterization of the weights for which localization on 5 sites occurs…

Message-passing architectures struggle to sufficiently model long-range dependencies in node and graph prediction tasks. We propose a novel approach exploiting hierarchical graph structures and adaptive random walks to address this…

Analyzing the mixing time of random walks is a well-studied problem with applications in random sampling and more recently in graph partitioning. In this work, we present new analysis of random walks and evolving sets using more…

We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…

We consider random walks in the form of nearest-neighbor hopping on Erdos-Renyi random graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this regime, using statistical field theory methods, we develop an…

In this paper, we propose and analyze a novel one-dimensional inhomogeneous random walk model that combines spatial decay of transition probabilities with a temporal renewal structure for each excursion. In this model, the probability of…

We study the biased random walk where at each step of a random walk a "controller" can, with a certain small probability, move the walk to an arbitrary neighbour. This model was introduced by Azar et al. [STOC'1992]; we extend their work to…

We consider branching random walks and contact processes on infinite, connected, locally finite graphs whose reproduction and infectivity rates across edges are inversely proportional to vertex degree. We show that when the ambient graph is…

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…

We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition…

We consider a class of strongly edge-reinforced random walks, where the corresponding reinforcement weight function is nondecreasing. It is known, from Limic and Tarr\`{e}s [Ann. Probab. (2007), to appear], that the attracting edge emerges…

We consider a vertex reinforced random walk on the integer lattice with sub-linear reinforcement. Under some assumptions on the regular variation of the weight function, we characterize whether the walk gets stuck on a finite interval. When…

Random walks find extensive application across various complex network domains, including embedding generation and link prediction. Despite the widespread utilization of random walks, the precise impact of distinct biases on embedding…

Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…

A rotor configuration on a graph contains in every vertex an infinite ordered sequence of rotors, each is pointing to a neighbor of the vertex. After sampling a configuration according to some probability measure, a rotor walk is a…

We consider a continuous-time vertex reinforced jump process on a supercritical Galton-Watson tree. This process takes values in the set of vertices of the tree and jumps to a neighboring vertex with rate proportional to the local time at…

In this thesis, we study three physically relevant models of strongly correlated random variables: trapped fermions, random matrices and random walks. In the first part, we show several exact mappings between the ground state of a trapped…

The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…