Kinetic Langevin processes with pure-jump Lévy noise satisfy strong Feller, irreducibility, spectral gap, and exponential ergodicity in low-regularity settings, with densities and C0-semigroup properties for alpha-stable cases.
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For asymmetric partial exclusion processes with product jump rates, the gradient condition is equivalent to product invariant measures, and fluctuations converge to the stationary energy solution of the stochastic Burgers equation.
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On some topological and spectral properties of kinetic Langevin processes driven by L{\'e}vy noises
Kinetic Langevin processes with pure-jump Lévy noise satisfy strong Feller, irreducibility, spectral gap, and exponential ergodicity in low-regularity settings, with densities and C0-semigroup properties for alpha-stable cases.
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Characterization of Gradient Condition for Asymmetric Partial Exclusion Processes and Their Scaling Limits
For asymmetric partial exclusion processes with product jump rates, the gradient condition is equivalent to product invariant measures, and fluctuations converge to the stationary energy solution of the stochastic Burgers equation.