# Probability

The research of the Probability Laboratory at Bath (Prob-L@B) spans the whole of modern probability, including models motivated by questions from other areas of mathematics as well as physics, biology, finance and other applied fields. We strongly encourage anyone interested in finding out more to investigate the webpages of the members of the Laboratory. Below is a brief introduction to some of the themes and objects that we study.

### Brownian motion

Random movement, observed by Brown as he watched pollen grains moving in water. Brownian motion is one of the objects at the very centre of probability theory and an important tool for building models of many random phenomena.

### Random graphs and networks

The world-wide web is just one modern example of the enormous networks that we encounter in our everyday lives.

### Self-organized criticality

Many phenomena in nature, such as earthquakes or avalanches, show mathematical order despite their chaotic nature. Self-organized criticality explains why this remarkable incongruity is, in many cases, inevitable.

### Interacting particle systems

Who will you vote for? Your decision is probably affected by the opinions of the people around you. In a similar way, many natural phenomena involve systems of particles that interact in complex ways.

### Lévy processes

Lévy processes describe microscopic movements that may jump suddenly from one location to another. They are used as the building blocks of more complex processes that are found in a variety of applied probability models.

### Mathematical finance

Understanding financial markets, including how to price assets and hedge risk, is important for everyone from supermarkets to government officials - not just stock market traders.

### Branching structures

Used to model family trees, computer algorithms and spread of disease, branching processes are vital to many areas of probability.

### Percolation

Imagine water seeping through the rock beneath your feet, or coffee through a filter: percolation is a basic mathematical model describing this process, and despite its simplicity holds an enduring fascination for probabilists.