# 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} }

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…

## 10 Citations

Exact and asymptotic properties of δ-records in the linear drift model

- Mathematics
- 2020

The study of records in the linear drift model (LDM) has attracted much attention recently due to applications in several fields. In the present paper we study δ-records in the LDM, defined as…

Statistical properties of avalanches via the
c
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We study the statistics of avalanches, as a response to an applied force, undergone by a particle hopping on a one dimensional lattice where the pinning forces at each site are independent and…

Record statistics of a strongly correlated time series: random walks and L\'evy flights

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- 2017

We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the…

Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics

- BiologybioRxiv
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This work introduces a broad class of high-dimensional random fitness landscapes for which the correlations between fitnesses of genomes are a general function of genetic distance, and studies the properties of these landscapes focusing on the simplest evolutionary process: random adaptive walks.

Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics.

- BiologyTheoretical population biology
- 2019

Universality Classes of Interaction Structures for NK Fitness Landscapes

- Biology
- 2017

A unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L is developed, and two different universality classes of interaction structures that display different asymptotics of this quantity for large k are identified.

Accessibility percolation in random fitness landscapes 3

- Biology
- 2019

This chapter reviews studies of accessibility percolation that use probabilistic fitness landscape models to explore the emergence of such paths as a function of the initial fitness, the parameters of the landscape or the structure of the genotype graph and discusses their implications for the predictability of evolutionary processes.

Accessibility percolation in random fitness landscapes

- Biology
- 2019

This chapter reviews studies of accessibility percolation that use probabilistic fitness landscape models to explore the emergence of paths as a function of the initial fitness, the parameters of the landscape or the structure of the genotype graph and discusses their implications for the predictability of evolutionary processes.

Genotypic Complexity of Fisher’s Geometric Model

- BiologyGenetics
- 2017

The analysis shows that thephenotypic dimension, which is often referred to as phenotypic complexity, does not generally correlate with the complexity of fitness landscapes and that even organisms with a single Phenotypic trait can have complex landscapes.

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