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Journal of the London Mathematical Society 2005 72(3):621-631; doi:10.1112/S0024610705006745
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© The London Mathematical Society

Comparison Theorems for the Spectral Gap of Diffusion Processes and Schrödinger Operators on an Interval

Ross G. Pinsky

Department of Mathematics, Technion-Israel Institute of Technology Haifa 32000, Israel pinsky{at}math.technion.ac.il

Received 20 April 2004.

The spectral gaps and thus the exponential rates of convergence to equilibrium are compared for ergodic one-dimensional diffusions on an interval. One of the results may be thought of as the diffusion analogue of a recent result for the spectral gap of one-dimensional Schrödinger operators. The similarities and differences between spectral gap results for diffusions and for Schrödinger operators are also discussed.


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