Discrete-time random walks and Lévy flights on arbitrary networks: when resetting becomes advantageous?

@article{Riascos2022DiscretetimeRW,
  title={Discrete-time random walks and L{\'e}vy flights on arbitrary networks: when resetting becomes advantageous?},
  author={Alejandro P. Riascos and Denis Boyer and Jos{\'e} L Mateos},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2022},
  volume={55}
}
The spectral theory of random walks on networks of arbitrary topology can be readily extended to study random walks and Lévy flights subject to resetting on these structures. When a discrete-time process is stochastically brought back from time to time to its starting node, the mean search time needed to reach another node of the network may be significantly decreased. In other cases, however, resetting is detrimental to search. Using the eigenvalues and eigenvectors of the transition matrix… 
The P\'{o}lya and Sisyphus lattice random walks with resetting -- a first passage under restart approach
TLDR
It is shown how the relatively direct approach used, First passage under restart for discrete space and time, could be generalized to arbitrary first passage process subject to more complex restart mechanisms such as sharp, Poisson and Zeta distribution where the latter is heavy tailed.

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