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Rescaled Whittaker driven stochastic differential equations converge to the additive stochastic heat equation
We study some linear SDEs arising from the two-dimensional $q$-Whittaker driven particle system on the torus as $q\to 1$. The main result proves that the SDEs along certain characteristics converge to the additive stochastic heat equation. Extensions for the SDEs with generalized coefficients and in other spatial dimensions are also …