# 2012 NZMRI/NZIMA Summer Workshop:

Random Media and Random Walks

This workshop will consist mainly of 6-8 mini-courses (3 50-minute talks) presented by distinguished international speakers, on some of the many interesting topics in probability theory and statistical physics. The workshop may be of interest to graduate students in probability, statistical physics, analysis, and discrete mathematics.

There will also be an evening of seminars in honour of**Prof. Peter Whittle**, on the evening of January 8, 2012. The theme of the seminars will be

*Stochastic modelling in physics, geophysics and communications.*

## Organisers

- Mark Holmes, Department of Statistics, the University of Auckland mholmes@stat.auckland.ac.nz

- Vaughan Jones

- Gaven Martin

## List of speakers

- Martin Barlow (U. British Columbia): Random walks on random graphs
- Geoffrey Grimmett (U. Cambridge): Percolation
- Remco van der Hofstad (T.U. Eindhoven, Eurandom): Random graphs
- Frank den Hollander (U. Leiden): Random walk in random environment
- Vlada Limic (CMI, U. de Provence): Reinforced random walks
- Tom Salisbury (York U.): Branching random walk and super-Brownian motion
- Vladas Sidoravicius (CWI Amsterdam, IMPA): Spatial processes with unbounded interactions

Many models of random media exhibit phase transitions. Bond percolation on the 2-dimensional square lattice is a relatively simple model to explain: For each pair of neighbours in the lattice, set the bond linking them to be occupied with probability p and vacant otherwise. Is it possible for the origin (0,0) to be connected to infinity by occupied bonds? The answer is yes precisely when p is greater than 1/2 | Excited random walks are random walks that have a bias (given by a single parameter b) to the right whenever they visit a site for the first time. Does such a random walk move with positive speed to the right? Does the speed increase with the bias parameter? The answer is yes to the former (in 2 and higher dimensions), while the latter has been proved only in high dimensions. |

## **Reading material**

Participants will be expected to have a solid general mathematics background, such as an honours degree in mathematics, including a course in probability or stochastic processes at the senior undergraduate level. Participants should also be comfortable with the following terms (all of which can be found for example in Grimmett and Stirzaker "Probability and Random Processes"):
Conditional probability, independence, random variables (discrete and continuous), expectation/expected values, Markov chains.
## **Conference Location**

All lectures will be in the Tahuna beach holiday park conference centre. Very close to Nelson airport (I walked from the airport, but this is not advisable if your luggage is substantial).

## **Timetable and format**

Talks start Sunday 8 January and end Friday 13 January, 2012. Timetable

## **Accommodation**

There are plenty of options. We have booked basic accommodation at Tahuna Beach Holiday Park, where the conference centre is located, as well as standard hotel/motel rooms at Beachcomber motor inn which is a 5-10 minute walk from the conference location. At the park there are basic cabins with shared facilities at $50 per cabin (for 2 people, or $35 for one person) per night. At Beachcomber rooms will be about $135 per night (for 1-2 people). **There are just 7 motel rooms remaining. Holiday park cabins are still available.**You may of course choose other accommodation if you wish. We will cover the cost of accommodation (holiday park cabins for students, otherwise Beachcomber or equivalent while room availability lasts) for NZ based participants. We will also cover the travel costs of NZ based students. Other attendees are expected to cover their own costs.

*Prices listed are in NZ$ as of January 2011.*