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Probability theory and related fields, 2022-06, Vol.183 (1-2), p.229-253
Ort / Verlag
Berlin/Heidelberg: Springer Berlin Heidelberg
Erscheinungsjahr
2022
Quelle
EBSCOhost Business Source Ultimate
Beschreibungen/Notizen
This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP) on a segment of length
N
. Our main result is that for particle densities in (0, 1), the total-variation cutoff window of ASEP is
N
1
/
3
and the cutoff profile is
1
-
F
GUE
,
where
F
GUE
is the Tracy-Widom distribution function. This also gives a new proof of the cutoff itself, shown earlier by Labbé and Lacoin. Our proof combines coupling arguments, the result of Tracy–Widom about fluctuations of ASEP started from the step initial condition, and exact algebraic identities coming from interpreting the multi-species ASEP as a random walk on a Hecke algebra.