Displaying similar documents to “Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach.”

Small eigenvalues of the Neumann realization of the semiclassical Witten Laplacian

D. Le Peutrec (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

This article follows the previous works [HeKlNi, HeNi] by Helffer-Klein-Nier and Helffer-Nier about the metastability in reversible diffusion processes via a Witten complex approach. Again, exponentially small eigenvalues of some self-adjoint realization of Δ f , h ( 0 ) = - h 2 Δ + ∇ f ( x ) 2 - h Δ f ( x ) are considered as the small parameter h > 0 tends to 0 . The function f is assumed to be a Morse function on some bounded domain Ω with boundary ∂ Ω . Neumann type boundary conditions are considered. With these boundary conditions, some...

L 2 -estimates for the d -equation and Witten’s proof of the Morse inequalities

Bo Berndtsson (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

This is an introduction to Witten’s analytic proof of the Morse inequalities. The text is directed primarily to readers whose main interest is in complex analysis, and the similarities to Hörmander’s L 2 -estimates for the ∂ ¯ -equation is used as motivation. We also use the method to prove L 2 -estimates for the d -equation with a weight e - t φ where φ is a nondegenerate Morse function.