# Generalised matrix Ansatz and exact current fluctuations in the open ASEP

#### Generalised matrix Ansatz and exact current fluctuations in the open ASEP

- Event time: 11:30am
- Event date: 21st November 2012
- Speaker: Alexandre Lazarescu (University of Luxembourg)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB

### Event details

The asymmetric simple exclusion process (ASEP) is one of the simplest, and yet one of the most studied models in non-equilibrium statistical physics. It is also related, more or less closely, to problems in biophysics (such as ribosomes moving on a m-RNA, which is what it was originally meant to describe), growing interfaces, pedestrian and car traffic, quantum spin chains, and many more. In this seminar, I will show how, by using a method based on Derrida, Evans, Hakim and Pasquier's matrix Ansatz, one can obtain the exact fluctuation statistics of the current of particles that characterises the steady state of the ASEP, for any finite size and any values of the parameters. I will then analyze the behaviour of these fluctuations in the large size limit. Finally, if time allows, I will discuss what other quantities we might be able to access using this method. Refs : J. Phys. A: Math. Theor. 44 (2011) 315001 , Phys. Rev. Lett. 109, 170601 (2012)

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