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April 2017 A piecewise deterministic scaling limit of lifted Metropolis–Hastings in the Curie–Weiss model
Joris Bierkens, Gareth Roberts
Ann. Appl. Probab. 27(2): 846-882 (April 2017). DOI: 10.1214/16-AAP1217

Abstract

In Turitsyn, Chertkov and Vucelja [Phys. D 240 (2011) 410–414] a nonreversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis–Hastings (LMH). A scaling limit of the magnetization process in the Curie–Weiss model is derived for LMH, as well as for Metropolis–Hastings (MH). The required jump rate in the high (supercritical) temperature regime equals $n^{1/2}$ for LMH, which should be compared to $n$ for MH. At the critical temperature, the required jump rate equals $n^{3/4}$ for LMH and $n^{3/2}$ for MH, in agreement with experimental results of Turitsyn, Chertkov and Vucelja (2011). The scaling limit of LMH turns out to be a nonreversible piecewise deterministic exponentially ergodic “zig-zag” Markov process.

Citation

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Joris Bierkens. Gareth Roberts. "A piecewise deterministic scaling limit of lifted Metropolis–Hastings in the Curie–Weiss model." Ann. Appl. Probab. 27 (2) 846 - 882, April 2017. https://doi.org/10.1214/16-AAP1217

Information

Received: 1 July 2015; Revised: 1 March 2016; Published: April 2017
First available in Project Euclid: 26 May 2017

zbMATH: 1370.60039
MathSciNet: MR3655855
Digital Object Identifier: 10.1214/16-AAP1217

Subjects:
Primary: 60F05
Secondary: 65C05

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.27 • No. 2 • April 2017
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