14:10
Particle current is the net number of particles that pass an observer who moves with a deterministic velocity V. Its fluctuations in time-stationary interacting particle systems are nontrivial and draw serious attention. It has been known for a while that in most models diffusive scaling and the corresponding Central Limit Theorem hold for this quantity. However, such normal fluctuations disappear for a particular value of V, called the characteristic speed.
For this velocity value, the correct scaling of particle current fluctuations was shown to be t1/3 and the limit distribution was also identified by K. Johansson in 2000 and later by P. L. Ferrari and H. Spohn in 2006. These results use heavy combinatorial and analytic tools, and their application is limited to a few particular models, one of which is the totally asymmetric simple exclusion process (TASEP). I will explain a purely probabilistic, more robust approach that provides the t2/3-scaling of current variance, but not the limit distribution, in (non-totally) asymmetric simple exclusion (ASEP) and some other particle systems. I will also point out a key feature of the models which allows the proof of such universal behaviour.
Joint work with Júlia Komjáthy and Timo Seppälläinen)