A determinantal formula for the GOE Tracy-Widom distribution
Patrik L. Ferrari (1), Herbert Spohn (1) ((1) TU-Muenchen)
TL;DR
This paper confirms that Sasamoto's new formula for the GOE Tracy-Widom distribution aligns with traditional formulas, advancing understanding of the distribution's properties in stochastic processes.
Contribution
It proves the equivalence of Sasamoto's determinantal formula with established expressions for the GOE Tracy-Widom distribution.
Findings
Sasamoto's formula is mathematically equivalent to standard formulas.
The work validates a new approach to the GOE Tracy-Widom distribution.
The results enhance analytical tools for studying stochastic growth models.
Abstract
Investigating the long time asymptotics of the totally asymmetric simple exclusion process, Sasamoto obtains rather indirectly a formula for the GOE Tracy-Widom distribution. We establish that his novel formula indeed agrees with more standard expressions.
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