The Continuous Time Random Walk, still trendy: Fifty-year history, state of art, and outlook

TL;DR

This paper reviews the fifty-year development of the continuous-time random walk (CTRW) formalism, highlighting its versatility, modifications, and broad applications across various fields, while discussing future perspectives.

Contribution

It provides a comprehensive overview of CTRW's evolution, current state, and potential future directions, emphasizing its ongoing relevance and adaptability.

Findings

CTRW has been influential in modeling complex systems.

Numerous modifications enhance CTRW's applicability.

Future perspectives suggest expanding CTRW's role in interdisciplinary research.

Abstract

In this issue we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism and its numerous modifications thanks to their flexibility and various applications as well its promising perspectives in different fields of knowledge. A short review of significant achievements and possibilities is given, however, still far from completeness.