On random unimodular lattices, full-sign Gibbs mass of e^{a/n}-edge windows vanishes for c≤1 and converges to a Poisson–Dirichlet partition for c>1; primitive fixed-γ windows have visibility threshold c=γ^{-2} in the high-temperature regime.
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Ajtai, Generating hard instances of lattice problems, extended abstract, in Proceedings of the 28th ACM Symposium on Theory of Computing, ACM, 1996, pp
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Quantum rejection sampling yields a quadratically faster discrete Gaussian sampler on lattices, enabling two improved versions of quantum dual attacks with trade-offs in speed and memory.
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Thermal Concentration and Poisson-Dirichlet Edge Statistics for Random-Lattice Gibbs Ensembles
On random unimodular lattices, full-sign Gibbs mass of e^{a/n}-edge windows vanishes for c≤1 and converges to a Poisson–Dirichlet partition for c>1; primitive fixed-γ windows have visibility threshold c=γ^{-2} in the high-temperature regime.
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Quantum algorithm for Discrete Gaussian Sampling
Quantum rejection sampling yields a quadratically faster discrete Gaussian sampler on lattices, enabling two improved versions of quantum dual attacks with trade-offs in speed and memory.