Related papers: Random walks on complex networks under time-depend…
We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic…
We derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only…
We introduce and study a metapopulation model of random walkers interacting at the nodes of a complex network. The model integrates random relocation moves over the links of the network with local interactions depending on the node…
We study in-network computation on general network topologies. Specifically, we are given the description of a function, and a network with distinct nodes at which the operands of the function are made available, and a designated sink where…
We replicate a renewal process at random times, which is equivalent to nesting two renewal processes, or considering a renewal process subject to stochastic resetting. We investigate the consequences on the statistical properties of the…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Classical first passage under resetting is a paradigm in the search process. Despite its multitude of applications across interdisciplinary sciences, experimental realizations of such resetting processes posit practical challenges in…
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},…
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…
We present an analytical method for computing the mean cover time of a random walk process on arbitrary, complex networks. The cover time is defined as the time a random walker requires to visit every node in the network at least once. This…
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks are characterized by the fact that the one-step transition probabilities are functions of the…
In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonous…
We consider a discrete-time continuous-space random walk, with a symmetric jump distribution, under stochastic resetting. Associated with the random walker are cost functions for jumps and resets, and we calculate the distribution of the…
We introduce a formalism based on a continuous time approximation, to study the characteristics of Page Rank random walks. We find that the diffusion of the occupancy probability has a dynamics that exponentially "forgets" the initial…
We propose local-biased random walks on general networks where a Markovian walker can choose between different types of biases in each node to define transitions to its neighbors depending on their degrees. For this ergodic dynamics, we…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
The paper investigates efficient distributed computation in dynamic networks in which the network topology changes (arbitrarily) from round to round. Our first contribution is a rigorous framework for design and analysis of distributed…
Stochastic resetting -- the intermittent restart of random processes -- has profoundly reshaped first-passage theory, providing a mechanism to control and optimize completion times. While the influence of resetting on mean first-passage…
It is known that the stationary distribution of the random walk process is dependent on the structure of the network. This could provide us a solution of the network reconstruction. However, the stationary distribution of the random walk…
We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized…