Submitted & Accepted Papers
Article: SHARP SPECTRAL GAP FOR DEGENERATED WITTEN LAPLACIAN
We consider the Witten Laplacian associated to a non-Morse potential. We prove Eyring–Kramers formulas for the bottom of the spectrum of this operator in the semiclassical regime and quantify the spectral gap between these eigenvalues and the rest of the spectrum. The main ingredient is the construction of sharp degenerated Gaussian quasimodes through an adaptation of the WKB method.
Article: SHARP SPECTRAL GAP OF ADAPTIVE LANGEVIN DYNAMICS
We consider a degenerated Fokker-Planck type differential operator as- sociated to an adaptive Langevin dynamic. We prove Eyring–Kramers formulas for the bottom of the spectrum of this operator in the low temperature regime. The main ingredients are resolvent estimates obtained via hypocoercive techniques and the construction of sharp Gaussian quasimodes through an adaptation of the WKB method