COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

## How to initialise a second class particle?Add to your list(s) Download to your calendar using vCal - Marton Balazs (Bristol)
- Tuesday 17 November 2015, 15:00-16:00
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
If you have a question about this talk, please contact Perla Sousi. This talk will be on interacting particle systems. One of the best known models in the field is the simple exclusion process where every site has 0 or 1 particles. It has long been established that under certain rescaling procedure this process converges to solutions of a deterministic nonlinear PDE (Burger’s equation). Particular types of solutions, called rarefaction fans, arise from decreasing step initial data. Second class particles are probabilistic objects that come from coupling two interacting particle systems. They are very useful and their behaviour is highly nontrivial. The beautiful paper of P. A. Ferrari and C. Kipnis connects the above: they proved that the second class particle of simple exclusion chooses a uniform random velocity when started in a rarefaction fan. The extremely elegant proof is based, among other ideas, on the fact that increasing the mean of a Bernoulli distribution can be done by adding or not adding 1 to the random variable. For a long time simple exclusion was the only model with an established large scale behaviour of the second class particle in its rarefaction fan. I will explain how this is done in the Ferrari-Kipnis paper, then show how to do this for other models that allow more than one particles per site. The main issue is that most families of distributions are not as nice as Bernoulli in terms of increasing their parameter by just adding or not adding 1. To overcome this we use a signed, non-probabilistic coupling measure that nevertheless points out a canonical initial probability distribution for the second class particle. We can then use this initial distribution to greatly generalize the Ferrari-Kipnis argument. I will conclude with an example where the second class particle velocity has a mixed discrete and continuous distribution. Joint work with Attila László Nagy This talk is part of the Probability series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS info aggregator
- DPMMS lists
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB
- Probability
- School of Physical Sciences
- Statistical Laboratory info aggregator
- bld31
Note that ex-directory lists are not shown. |
## Other listsChemical Engineering and Biotechnology Departmental Seminars women@CL all Epigenetics and Stem Cells 2012## Other talksRecovery conditions of compressed sensing approach to uncertainty quantification Locomotion in extinct giant kangaroos? Hopping for resolution. Participatory approaches to encourage responsible use of antibiotics in livestock Calcium signalling in bipolar disorder - new twists to an old story Slaying (or at least taming) a dreadful monster: Louis de Serres' treatise of 1625 for women suffering from infertility Religion, revelry and resistance in Jacobean Lancashire |