A general mixing criterion shows which random transports preserve asymptotic variance, yielding a procedure that turns any ergodic point process into a hyperuniform one.
The two-dimensional one-component plasma is hyperuniform
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We prove that at all positive temperatures in the bulk of a classical two-dimensional one-component plasma (also called Coulomb or log-gas, or jellium) the variance of the number of particles in large disks grows (strictly) more slowly than the area. In other words the system is hyperuniform.
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Invariant transports of stationary random measures: asymptotic variance, hyperuniformity, and examples
A general mixing criterion shows which random transports preserve asymptotic variance, yielding a procedure that turns any ergodic point process into a hyperuniform one.