Under simple growth conditions on the potential and mirror map, Mirror Langevin diffusions satisfy Poincaré or log-Sobolev inequalities, and a new exactly-stationary Gibbs sampler converges weakly to the diffusion and mixes in chi-square at rate (1 - c0*epsilon)^k.
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Mirror Langevin diffusions: Convergence rates and Markov chain approximations
Under simple growth conditions on the potential and mirror map, Mirror Langevin diffusions satisfy Poincaré or log-Sobolev inequalities, and a new exactly-stationary Gibbs sampler converges weakly to the diffusion and mixes in chi-square at rate (1 - c0*epsilon)^k.