Renormalization group theory for percolation in time-varying networks

Area of Science:

• Network Science
• Statistical Physics
• Wireless Communication

Background:

• Unreliable wireless networks face challenges with multi-hop communication.
• Dynamic network conditions, where links change state, complicate path reliability.
• Classical percolation theory is limited in analyzing time-varying network dynamics.

Purpose of the Study:

• To extend percolation theory to time-varying networks.
• To analyze the temporal correlations of message losses in multi-hop wireless communication.
• To provide a theoretical framework for designing robust wireless protocols.

Main Methods:

• Developed a renormalization group theory for stochastic link dynamics on a grid.
• Mapped the temporal path existence problem to a two-state Markov process.
• Analyzed the convergence of the Markov process to a memoryless Bernoulli process.

Main Results:

• The temporal existence of multi-hop paths is modeled as an effective Markov process.
• The Markov process converges to a memoryless Bernoulli process as hop distance increases.
• Temporal correlations in message losses are analytically elucidated.

Conclusions:

• The extended percolation theory accurately models dynamic wireless networks.
• Understanding temporal correlations is crucial for improving wireless communication and control protocols.
• Findings have implications for cyber-physical systems like drone swarms and smart traffic networks.