# A mean first passage time genome rearrangement distance

## TL;DR

This paper proposes a novel genome rearrangement distance based on mean first passage time, establishing a true metric on genome space and connecting it to graph zeta functions, applicable across various models of genome evolution.

## Contribution

It introduces a new distance measure for genomes using mean first passage time, linking it to graph theory and broadening its applicability in genome evolution models.

## Key findings

- Defines a genuine metric for genome rearrangement distance
- Establishes a theoretical link to graph zeta functions
- Applicable to diverse group-theoretic genome evolution models

## Abstract

This paper introduces a new way to define a genome rearrangement distance, using the concept of mean first passage time from probability theory. Crucially, this distance estimate provides a genuine metric on genome space. We develop the theory and introduce a link to a graph-based zeta function. The approach is very general and can be applied to a wide variety of group-theoretic models of genome evolution.