# 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: Mathematical and Theoretical},
year={2016},
volume={49}
}
• Published 16 March 2016
• Mathematics
• Journal of Physics A: Mathematical and Theoretical
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 Y k > Y k − 1 − δ k − 1 with a deterministic sequence δ k > 0 called the handicap. For constant δ k ≡ δ 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…
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