Real diffusion with complex spectral gap

2023/10/06 by Bony, Jean-Francois, Michel, Laurent · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2310.04203

Abstract

The low-lying eigenvalues of the generator of a Langevin process are known to satisfy the Eyring-Kramers law in the low temperature regime under suitable assumptions. These eigenvalues are generically real. We construct generators whose spectral gap is given by non-real eigenvalues or by a real eigenvalue having a Jordan block.

Cited by

• Eyring-Kramers formula for the mean exit time of non-Gibbsian elliptic processes: the non characteristic boundary case

Related

• Quantitative low-temperature spectral asymptotics for reversible diffusions in temperature-dependent domains
• Sharp spectral gap of adaptive Langevin dynamics
• Eyring-Kramers law for Fokker-Planck type differential operators
• An Eyring--Kramers Law for the Hypoelliptic Third-Order Langevin Diffusion
• Langevin Diffusion Approximation to Same Marginal Schrödinger Bridge