# Record statistics for a discrete-time random walk with correlated steps

## TL;DR

This paper analyzes record statistics in a correlated discrete-time random walk, revealing how long-term memory and correlations influence record events and differ from independent step models.

## Contribution

It provides exact calculations of record-related quantities for a correlated random walk, highlighting novel behaviors due to strong correlations.

## Key findings

- Correlations induce super-diffusivity and transience.
- Record statistics differ significantly from independent step walks.
- Exact formulas for record-related quantities are derived.

## Abstract

The characterization of record events is considered for a discrete-time random walk model with long-term memory arising from correlations between successive steps. An important feature is that the correlations are strong enough to give rise to super-diffusivity and transience. Various quantities related to record statistics are calculated exactly, highlighting important differences in behaviour from the simple random walk with independent steps.

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Source: https://tomesphere.com/paper/1905.13013