Selected problems in probability theory

TL;DR

This paper presents a personal selection of open problems in discrete probability theory, including questions on Lorentz scatterers, self-avoiding walks, and percolation, aiming to inspire further research.

Contribution

It offers a curated list of open problems in probability theory, highlighting less-explored areas and encouraging ongoing investigation.

Findings

Identifies key open problems in Lorentz scatterers and self-avoiding walks.

Highlights challenges in percolation theory.

Provides insights to stimulate future research.

Abstract

This celebratory article contains a personal and idiosyncratic selection of a few open problems in discrete probability theory. These include certain well known questions concerning Lorentz scatterers and self-avoiding walks, and also some problems of percolation-type. The author hopes the reader will find something to leaven winter evenings, and perhaps even a project for the longer term.