Recovery Random Walks for Extreme Events on Complex Networks

Abstract

Extreme events are widely studied within simple random walk frameworks, where their probability is determined by the network structure and stationary walker distribution. Here, we propose a recovery random walk (RRW) model in which extreme events temporally `freeze' the nodes where they occur for a fixed duration Δ (Δ=0 recovers the original model), trapping walkers and reducing the effective mobile population, thereby making the model more practical. We derive a first-principles description of this feedback and a delayed differential equation for the frozen-node fraction. This finite freezing produces an initial overshoot, followed by damped oscillatory relaxation to a steady state for the fraction of the frozen nodes. We find that freezing suppresses extreme event probability while preserving its degree dependence dynamics, and suppresses the EE frequency. Further, the analytical prediction for the fraction of the frozen nodes agrees closely with simulations. This model closely reflects real-world scenarios, yielding more practical EE statistics.

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BibTeX RIS

BibTeX

@misc{singh2026recovery,
  title = {{Recovery Random Walks for Extreme Events on Complex Networks}},
  author = {Karan Singh and Narendran R. V. and V. K. Chandrasekar and D. V. Senthilkumar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.39377},
  eprint = {2609.39377},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39377},
}

RIS

TY  - UNPB
TI  - Recovery Random Walks for Extreme Events on Complex Networks
AU  - Karan Singh
AU  - Narendran R. V.
AU  - V. K. Chandrasekar
AU  - D. V. Senthilkumar
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.39377
UR  - https://arxiv.org/abs/2609.39377
AB  - Extreme events are widely studied within simple random walk frameworks, where their probability is determined by the network structure and stationary walker distribution. Here, we propose a recovery random walk (RRW) model in which extreme events temporally `freeze' the nodes where they occur for a fixed duration Δ (Δ=0 recovers the original model), trapping walkers and reducing the effective mobile population, thereby making the model more practical. We derive a first-principles description of this feedback and a delayed differential equation for the frozen-node fraction. This finite freezing produces an initial overshoot, followed by damped oscillatory relaxation to a steady state for the fraction of the frozen nodes. We find that freezing suppresses extreme event probability while preserving its degree dependence dynamics, and suppresses the EE frequency. Further, the analytical prediction for the fraction of the frozen nodes agrees closely with simulations. This model closely reflects real-world scenarios, yielding more practical EE statistics.
ER  -

Abstract

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