The 1D stochastic Allen-Cahn equation with localized white noise admits a unique invariant measure and its Markov process is exponentially mixing.
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General quantitative conditions are established for the existence of a unique invariant probability measure and exponential ergodicity of Markov semigroups for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise, together with moment estimates and Wasserst
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Exponential mixing for the stochastic Allen--Cahn equation with localized white noise
The 1D stochastic Allen-Cahn equation with localized white noise admits a unique invariant measure and its Markov process is exponentially mixing.
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Ergodicity and mixing for locally monotone stochastic evolution equations
General quantitative conditions are established for the existence of a unique invariant probability measure and exponential ergodicity of Markov semigroups for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise, together with moment estimates and Wasserst