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

## Self-organized criticalityMany 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 systemsWho 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 processesPath discontinuous stochastic processes describe microscopic movements that may jump suddenly from one location to another. |
## Mathematical financeUnderstanding financial markets, including how to price assets and hedge risk, is important for everyone from supermarkets to government officials. |

## Branching structuresUsed to model family trees, computer algorithms and spread of disease, branching processes are vital to many areas of probability. |
## PercolationImagine 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 probabilityCounting and understanding structures with particular properties has many applications, especially to computer science. |
## Monte Carlo simulationMonte Carlo algorithms are designed to solve deterministic problems using randomness. They are used everywhere, from nuclear physics to aerospace engineering. |