Accelerating Brownian motion on N-torus

Hui-Ming Pai and Chii-Ruey Hwang

Statistics & Probability Letters, 2013, vol. 83, issue 5, 1443-1447

Abstract: On N-torus, we consider antisymmetric perturbations of Laplacian of the form LC≐Δ+C⋅∇, where C is a divergence free vector field. The spectral gap, denoted by λ(C), of L(C) is defined by −sup{real part of μ,μ is in the spectrum ofLC, μ≠0}. We characterize for a certain class of C’s, the limit of λ(kC) as k goes to infinity and prove that sup{λ(C),C is divergence free}=∞. This problem is motivated by accelerating diffusions. By adding a weighted antisymmetric drift to a reversible diffusion, the convergence to the equilibrium is accelerated using the spectral gap as a comparison criterion. However, how good can the improvement be is yet to be answered. In this paper, we demonstrate that on N-torus the acceleration of Brownian motion could be infinitely fast.

Keywords: Spectral gap; Antisymmetric perturbation; Torus; Convergence rate; Diffusions (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2013.02.009

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