A Pfaffian representation for flat ASEP
Janosch Ortmann, Jeremy Quastel, Daniel Remenik
TL;DR
This paper derives a Pfaffian formula for the generating function of the height function in flat ASEP, connecting it to the GOE Tracy-Widom distribution through asymptotic analysis.
Contribution
It introduces a Pfaffian representation for flat ASEP's height function generating function, advancing the mathematical understanding of its distribution.
Findings
Fredholm Pfaffian formula for flat ASEP
Asymptotic analysis yields GOE Tracy-Widom distribution
Provides a new mathematical framework for ASEP height fluctuations
Abstract
We obtain a Fredholm Pfaffian formula for an appropriate generating function of the height function of the asymmetric simple exclusion process starting from flat (periodic) initial data. Formal asymptotics lead to the GOE Tracy-Widom distribution.
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