Work

Total variation bound for Kac’s random walk

Year: 2012

Type: article

Abstract: We show that the classical Kac’s random walk on $(n-1)$-sphere $S^{n-1}$ starting from the point mass at $e_{1}$ mixes in $\mathcal{O}(n^{5}(\log n)^{3})$ steps in total variation distance. The main argument uses a truncation of the running density after a burn-in period, followed by $\mathcal{L}^{2}$ convergence using the spectral gap information derived by other authors. This improves upon a previous bound by Diaconis and Saloff-Coste of order $\mathcal{O}(n^{2n})$.

Source: The Annals of Applied Probability

DOI: 10.1214/11-aap810

Author: Yunjiang Jiang

Institution: Stanford University

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

OpenAlex ID: W1965712937