Related papers: Universal adaptive self-stabilizing traversal sche…
We study the random walk problem on a class of deterministic Scale-Free networks displaying a degree sequence for hubs scaling as a power law with an exponent $\gamma=\log 3/\log2$. We find exact results concerning different first-passage…
We construct a quantum random walk algorithm, based on the Dirac operator instead of the Laplacian. The algorithm explores multiple evolutionary branches by superposition of states, and does not require the coin toss instruction of…
This paper considers non-backtracking random walks on random graphs generated according to the configuration model. The quantity of interest is the scaling of the mixing time of the random walk as the number of vertices of the random graph…
We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance…
When navigating complex environments, animals often combine multiple strategies to mitigate the effects of external disturbances. These modalities often correspond to different sources of information, leading to speed-accuracy trade-offs.…
Consider a sequence of i.i.d. random variables $X_n$ where each random variable is refreshed independently according to a Poisson clock. At any fixed time $t$ the law of the sequence is the same as for the sequence at time 0 but at random…
Will the strategy of resetting} help a stochastic process to reach its target efficiently, with its environment continually toggling between a strongly favourable and an unfavourable (or weakly favourable) state? A diffusive run-and-tumble…
Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…
Random walks in random scenery are processes defined by $Z_n:=\sum_{k=1}^n\xi_{X_1+...+X_k}$, where $(X_k,k\ge 1)$ and $(\xi_y,y\in\mathbb Z)$ are two independent sequences of i.i.d. random variables. We suppose that the distributions of…
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 consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
We study decentralized learning over networks where data are distributed across nodes without a central coordinator. Random walk learning is a token-based approach in which a single model is propagated across the network and updated at each…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the…
In this article, we present new random walk methods to solve flow and transport problems in unsaturated/saturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic…
A powerful strategy to accelerate quantum-walk-based search algorithms leverages on resetting protocols, where a detector monitors a target site and the evolution of the walker is restarted if no detection occurs within a fixed time…
We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability. We focus on the case when the time interval between subsequent…