# 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…

## One Citation

The P\'{o}lya and Sisyphus lattice random walks with resetting -- a first passage under restart approach

- Mathematics, Computer Science
- 2021

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.

## References

SHOWING 1-10 OF 12 REFERENCES

First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry.

- MathematicsPhysical review. E
- 2022

We investigate the first passage properties of a Brownian particle diffusing freely inside a d-dimensional sphere with absorbing spherical surface subject to stochastic resetting. We derive the mean…

Random Walks on Graphs: A Survey

- Mathematics
- 2001

Estimates on the important parameters of access time, commute time, cover time and mixing time are discussed and recent algorithmic applications of random walks are sketched, in particular to the problem of sampling.

Graph Spectra for Complex Networks

- Computer Science
- 2010

This self-contained book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks, and the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks.

Personalized PageRank with Node-Dependent Restart

- Computer Science, MathematicsWAW
- 2014

This work introduces two generalizations of Personalized PageRank with node-dependent restart and shows that both generalizations have an elegant expression connecting the so-called direct and reverse PersonalizedPageRank that yield a symmetry property of these Personalization PageRanks.

Algebraic Graph Theory

- MathematicsGraduate texts in mathematics
- 2001

The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.

Random Walks and Random Environments: Vol. 1: Random Walks (New

- 1995

Networks: An Introduction (Oxford

- 2010

Discrete-time random walks and Lévy flights on arbitrary networks

- J. Phys. A: Math. Theor
- 2019

Algebraic Graph Theory (Graduate Texts in Mathematics vol 207

- 2001