The lower tail of the half-space KPZ equation

Yujin H. Kim

Stochastic Processes and their Applications, 2021, vol. 142, issue C, 365-406

Abstract: We establish the first tight bound on the lower tail probability of the half-space KPZ equation with Neumann boundary parameter A=−1/2 and narrow-wedge initial data. The lower bound demonstrates a crossover between two regimes of super-exponential decay with exponents 52 and 3; the upper bound demonstrates a crossover between regimes with exponents 32 and 3. Given a crude leading-order asymptotic in the Stokes region for the Ablowitz–Segur solution to Painlevé II (Definition 1.8), we improve the upper bound to demonstrate the same crossover as the lower bound. We also establish novel bounds on the large deviations of the GOE point process.

Keywords: (Half-space) Kardar–Parisi–Zhang equation; Pfaffian point processes; GOE ensemble; Large deviations; Stochastic Airy operator; Ablowitz–Segur Solution to Painlevé II (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:142:y:2021:i:c:p:365-406

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DOI: 10.1016/j.spa.2021.09.001

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