Mean first-encounter times of simultaneous random walkers with resetting on networks

Abstract

We investigate the dynamics of simultaneous random walkers with resetting on networks and derive exact analytical expressions for the mean first-encounter times of Markovian random walkers. Specifically, we consider two cases for the simultaneous dynamics of two random walkers on networks: when only one walker resets to the initial node, and when both walkers return to their initial positions. In both cases, the encounter times are expressed in terms of the eigenvalues and eigenvectors of the transition matrix of the normal random walk, providing a spectral interpretation of the impact of resetting. We validate our approach through examples on rings, Cayley trees, and random networks generated using the Erdős-Rényi, Watts-Strogatz, and Barabási-Albert algorithms, where resetting significantly reduces encounter times. The proposed framework can be extended to other types of random walk dynamics, transport processes, or multiple-walker scenarios, with potential applications in human mobility, epidemic spreading, and search strategies in complex systems.

arXiv comment24 pages, 5 figures

References in corpus (43)

• Emergence of scaling in random networks
• Epidemic spreading in scale-free networks
• Diffusion with Stochastic Resetting
• Random walks and diffusion on networks
• Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys
• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• First order transition for the optimal search time of Lévy flights with resetting
• Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks
• Optimal stochastic restart renders fluctuations in first passage times universal
• Diffusion under time-dependent resetting
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Diffusion with stochastic resetting at power-law times
• Global mean first-passage times of random walks on complex networks
• First passage under stochastic resetting in an interval
• Optimal first arrival times in Lévy flights with resetting
• Stochastic Search with Poisson and Deterministic Resetting
• Monotonous continuous-time random walks with drift and stochastic reset events
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Long-Range Navigation on Complex Networks using Lévy Random Walks
• Random walks on networks with stochastic resetting
• Extreme events on complex networks
• Fractional dynamics on networks: Emergence of anomalous diffusion and Lévy flights
• Transport properties and first arrival statistics of random searches with stochastic reset times
• Spectral properties of simple classical and quantum reset processes
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• On subdiffusive continuous time random walks with stochastic resetting
• Extreme statistics and spacing distribution in a Brownian gas correlated by resetting
• Stochastic resetting in interacting particle systems: A review
• Diffusive transport on networks with stochastic resetting to multiple nodes
• Epidemic spreading on modular networks: The fear to declare a pandemic
• Random Multi-Hopper Model. Super-Fast Random Walks on Graphs
• Encounter times in overlapping domains: application to epidemic spread in a population of territorial animals
• A markovian random walk model of epidemic spreading
• The two-particle problem in comb-like structures
• From classical to quantum walks with stochastic resetting on networks
• Fractional random walk lattice dynamics
• Mean encounter times for multiple random walkers on networks
• Onset of anomalous diffusion from local motion rules
• Diffusion with two resetting points
• Critical number of walkers for diffusive search processes with resetting
• Random walks with stochastic resetting in complex networks: a discrete time approach
• Exact encounter times for many random walkers on regular and complex networks