Related papers: Random Walks with Traversal Costs: Variance-Aware …
We study a broad class of random labelled trees in which integer-valued labels evolve along the edges according to increments in $\{-1, 0, 1\}$. These models include e.g. branching random walks, embedded complete and incomplete binary…
Estimating characteristics of large graphs via sampling is a vital part of the study of complex networks. Current sampling methods such as (independent) random vertex and random walks are useful but have drawbacks. Random vertex sampling…
Random walks on networks are widely used to model stochastic processes such as search strategies, transportation problems or disease propagation. A prominent example of such process is the guiding of naive T cells by the lymph node conduits…
Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient…
Recently, De Martino et al have presented a general framework for the study of transportation phenomena on complex networks. One of their most significant achievements was a deeper understanding of the phase transition from the uncongested…
Rare event statistics for random walks on complex networks are investigated using the large deviations formalism. Within this formalism, rare events are realized as typical events in a suitably deformed path-ensemble, and their statistics…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
Let $X$ be a continuous time random walk on a weighted graph. Given the on-diagonal upper bounds of transition probabilities at two vertices $x_1$ and $x_2$, we use an adapted metric initiated by Davies, and obtain Gaussian upper estimates…
Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover…
Analysis of algorithms on time-varying networks (often called evolving graphs) is a modern challenge in theoretical computer science. The edge-Markovian is a relatively simple and comprehensive model of evolving graphs: every pair of…
We study random walk among random conductance (RWRC) on complete graphs with N vertices. The conductances are i.i.d. and the sum of conductances emanating from a single vertex asymptotically has an infinitely divisible distribution…
Kemeny's constant quantifies the expected time for a random walk to reach a randomly chosen vertex, providing insight into the global behavior of a Markov chain. We present a novel eigenvector-based formula for computing Kemeny's constant.…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…
We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…
Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…
We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…
We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours…
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…
Given a set of graphs from some unknown family, we want to generate new graphs from that family. Recent methods use diffusion on either graph embeddings or the discrete space of nodes and edges. However, simple changes to embeddings (say,…
Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical…