Random walks on graphs: ideas, techniques and results

TL;DR

This paper reviews recent mathematical advances and ideas in the study of random walks on graphs, emphasizing their physical implications and interdisciplinary applications.

Contribution

It provides a comprehensive overview of new results and ideas in random walks on graphs, highlighting their relevance across various scientific disciplines.

Findings

Recent mathematical results on random walks

Introduction of new ideas and techniques

Emphasis on physical aspects of graph processes

Abstract

Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and new ideas have been introduced, which can be fruitfully extended to different areas and disciplines. Here we aim at giving a brief but comprehensive perspective of these progresses, with a particular emphasis on physical aspects.