δ-exceedance records and random adaptive walks

@article{Park2016exceedanceRA,
  title={$\delta$-exceedance records and random adaptive walks},
  author={Su-Chan Park and Joachim H A Krug},
  journal={Journal of Physics A},
  year={2016},
  volume={49},
  pages={315601}
}
We study a modified record process where the kth record in a series of independent and identically distributed random variables is defined recursively through the condition with a deterministic sequence called the handicap. For constant and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of δ between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean… 
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