Convergences of the rescaled Whittaker stochastic differential equations and independent sums
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Bibliographic record
Abstract
We study some SDEs derived from the q→1 limit of a 2D surface growth model called the q-Whittaker process. The fluctuations are proven to exhibit Gaussian characteristics that “come down from infinity”: After rescaling and re-centering, convergences to the time-inverted stationary additive stochastic heat equation (SHE) hold. The point of view in this paper is a novel probabilistic representation of the SDEs by independent sums. By this connection, the normal and Poisson approximations, both in diverging integrated forms, explain the convergence of the re-centered covariance functions. The proof of the process-level convergence identifies additional divergent terms in the dynamics and considers nontrivial cancellations.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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