# Current Fluctuations in the Asymmetric Simple Exclusion Process and Bethe Ansatz - Part II

#### Current Fluctuations in the Asymmetric Simple Exclusion Process and Bethe Ansatz - Part II

- Event time: 2:00pm
- Event date: 30th September 2008
- Speaker: Sylvain Prolhac (University of Edinburgh)
- Location: Room 3315, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB

### Event details

In this second part, after recalling briefly how the Bethe Ansatz is used for the calculation of the current fluctuations in the asymmetric simple exclusion process on a ring, I will show that the Bethe equations can be conveniently rewritten as a functional equation. This functional equation can be solved exactly in the totally asymmetric case, giving access to the complete fluctuations of the current. For the general case of a partial asymmetry, a complete solution is not known: only the three first cumulants of the current have been calculated. I will discuss the two interesting scaling limits for which these cumulants take simple expressions. These two scaling limits can be understood by simple physical arguments.

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