Probability laboratory at Bath

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Prob-L@B

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

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.

Random graphs and networks

A random geometric graph

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

Self-organized criticality

A forest fire process

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

An interacting particle system

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.

Path discontinuous processes

Some Levy processes

Path discontinuous stochastic processes describe microscopic movements that may jump suddenly from one location to another.

Mathematical finance

Graph from mathematical finance

Understanding financial markets, including how to price assets and hedge risk, is important for everyone from supermarkets to government officials.

Branching structures

A branching process

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

Percolation

Percolation clusters

Imagine water seeping through the rock beneath your feet, or coffee through a filter: percolation describes this process, and holds an enduring fascination for probabilists.

Combinatorial probability

An Erdos-Renyi graph

Counting and understanding structures with particular properties has many applications, especially to computer science.

Monte Carlo simulation

The output of an MCMC algorithm

Monte Carlo algorithms are designed to solve deterministic problems using randomness. They are used everywhere, from nuclear physics to aerospace engineering.