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Cutoff and discrete product structure in ASEP

Date: Thursday, February 7, 2019 16:15 - 18:15
Speaker: Peter Nejjar (IST Austria)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Lazlo Erdös
Contact: Caroline Petz
Lab building west seminar room

Abstract:

We consider the asymmetric simple exclusion process (ASEP) on Z with an initial data such that in the large time particle density ρ(·) a discontinuity at the origin is created, where the value of ρ jumps from zero to one, but ρ(−ε),1 − ρ(ε) > 0 for any ε > 0. We consider the position of a particle xM macroscopically located at the discontinuity, and show that its limit law has a cutoff under t1/2 scaling. Inside the discontinuity region, we show that a discrete product limit law arises, which bounds from above the limiting fluctuations of xM in the general ASEP, and equals them in the totally ASEP. Sending M → ∞, the discrete product limit law converges to FGUE × FGUE, which was previously observed at shocks in TASEP.

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