| Abstract: |
| In this talk, we consider the scaling limit of the one-dimensional lattice Ising--Kac--Kawasaki dynamics
under conservative Kawasaki exchange rate.
For the Kac coarse-grained field \(X_\gamma\), we derive a martingale formulation with a
discrete conservative drift and a Dynkin martingale.
The nonlinear drift is identified by a conservative multiscale replacement scheme based on
one-block/two-block estimates, yielding a cubic conservative term in the macroscopic equation.
For the stochastic part, we compute the predictable quadratic variation, and obtain a divergence-form Gaussian noise.
As a consequence, \(X_\gamma\) converges to a one-dimensional stochastic Cahn--Hilliard equation with conserved noise. |
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