Abstract

The name “Grushin problem” refers here to the variation of Schur complement technique introduced by J. Sjöstrand in his early works, which is now a commonly used tool in spectral analysis (see Acta. Math. 130 (1973), 1–51 and Ann. Inst. Fourier 57:7 (2007), 2095–2141). Recently Q. Ren and Z. Tao proposed such an approach for the analysis of the low-lying eigenvalues in the large friction limit for a simple scalar kinetic model. Inspired by this work and the introduction of functional spaces adapted to the analysis of geometric Kramers–Fokker–Planck operators in a previous article, here we study the combined asymptotic analysis of Bismut’s hypoelliptic Laplacian in the high friction $b\to 0^{+}$ and possibly low temperature $h\to 0^{+}$ regimes.

Keywords

Mathematical Subject Classification

Milestones

Authors