Small-ball spectral convergence for sub-Riemannian diffusions

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A sub-Riemannian diffusion killed when it exits a sufficiently small metric ball is expected to exhibit an analogous small-ball spectral convergence to the corresponding nilpotent or tangent diffusion. Small-ball spectral convergence conjecture. A similar result should hold for more general sub-Riemannian diffusions killed at exiting a small metric ball. This would extend the convergence of the re-normalized Dirichlet eigenvalues established here for small balls in SU⁡(2)\operatorname{SU}(2) to a broader class of sub-Riemannian diffusions, but the source does not specify the precise hypotheses or formulate the corresponding limiting spectrum.

References

Primary source

Marco Carfagnini, Maria Gordina and Alexander Teplyaev, “Dirichlet metric measure spaces: spectrum, irreducibility, and small deviations”, arXiv:2409.07425 (2024).

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