Record statistics for random walks and Lévy flights with resetting

@article{Majumdar2021RecordSF,
  title={Record statistics for random walks and L{\'e}vy flights with resetting},
  author={Satya N. Majumdar and Philippe Mounaix and Sanjib Sabhapandit and Gr{\'e}gory Schehr},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={55}
}
We compute exactly the mean number of records ⟨R N ⟩ for a time-series of size N whose entries represent the positions of a discrete time random walker on the line with resetting. At each time step, the walker jumps by a length η drawn independently from a symmetric and continuous distribution f(η) with probability 1 − r (with 0 ⩽ r < 1) and with the complementary probability r it resets to its starting point x = 0. This is an exactly solvable example of a weakly correlated time-series that… 
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Contents: Preface * Preliminaries * Domains of Attraction and Norming Constants * Quality of Convergence * Point Processes * Records and Extremal Processes * Multivariate Extremes * References *
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