Steady state and mean recurrence time for random walks on stochastic temporal networks

Area of Science:

• Network science
• Statistical physics
• Complex systems

Background:

• Random walks are fundamental diffusion processes on networks.
• Temporal network dynamics significantly impact random walk behavior.
• Understanding event-driven walks is crucial for network analysis.

Purpose of the Study:

• To theoretically analyze two event-driven random walks on stochastic temporal networks.
• To investigate the influence of interevent time distributions on walk properties.
• To compare active and passive random walk behaviors.

Main Methods:

• Modeling stochastic temporal networks with arbitrary interevent time distributions.
• Developing theoretical frameworks for active and passive random walks.
• Analyzing steady-state distributions and mean recurrence times.

Main Results:

• Passive random walks exhibit a uniform steady-state node density.
• Active random walks' steady-state density depends on node degree and interevent time distribution.
• Mean recurrence time is inversely proportional to node degree for both walk types.

Conclusions:

• The choice between active and passive random walks significantly alters network diffusion properties.
• Interevent time distributions critically influence active random walks but not passive ones.
• Both walk types show degree-dependent mean recurrence times.