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Random walks on complex networks with first-passage resetting.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Random walks are fundamental models for diffusion and exploration on networks.
  • First-passage processes describe the time taken to reach a target state.
  • Network resetting mechanisms can alter search dynamics and efficiency.

Purpose of the Study:

  • To investigate the impact of first-passage resetting on discrete-time random walks on arbitrary networks.
  • To derive analytical expressions for key quantities like stationary occupation probability and mean first-passage time.
  • To demonstrate the advantages of first-passage resetting for global search strategies.

Main Methods:

  • Formulating a discrete-time random walk model with first-passage resetting.
  • Defining observable and resetting nodes within the network.
  • Deriving exact expressions using the fundamental matrix Z = (I-Q)^{-1} for non-observable nodes.
  • Analyzing performance on various network topologies (ring, lattice, barbell, Cayley tree).

Main Results:

  • Exact expressions for stationary occupation probability and average number of resets were derived.
  • Mean first-passage times between non-observable nodes were analytically determined.
  • The fundamental matrix of the non-observable nodes' transition matrix is key to these calculations.
  • First-passage resetting was shown to improve global search performance across diverse networks.

Conclusions:

  • First-passage resetting provides an effective mechanism to control and enhance random walk dynamics on networks.
  • The analytical framework based on the fundamental matrix offers a powerful tool for understanding such processes.
  • This resetting strategy demonstrates significant advantages for global search problems in complex network environments.