Abstract
The purpose of this article is to investigate the continuum limit of a distributional identity for half-space directed polymers given in [BBC20]. The limiting identity turns out to relate the multiplicative-noise half-space stochastic heat equation with Dirichlet boundary condition to the same equation with Robin boundary condition. The identity is related to conjectured Gaussian fluctuation behavior of subcritical half-space KPZ.
Funding Statement
The author was partially supported by the Fernholz Foundation’s “Summer Minerva Fellows” program, as well as summer support from Ivan Corwin’s NSF grant DMS:1811143.
Acknowledgments
Foremost, the author is tremendously grateful to two anonymous referees who gave extremely diligent reports, recommendations, and errata relating to the original article. We thank Ivan Corwin for suggesting that interesting identities could potentially be obtained from results in [BBC20], and also for reading portions of the preliminary draft. We also thank Yier Lin for pointing out a mistake in some of the estimates.
Citation
Shalin Parekh. "Positive random walks and an identity for half-space SPDEs." Electron. J. Probab. 27 1 - 47, 2022. https://doi.org/10.1214/22-EJP775
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