A piecewise deterministic scaling limit of lifted Metropolis-Hastings in the Curie-Weiss model

DOI10.1214/16-AAP1217zbMATH Open1370.60039arXiv1509.00302MaRDI QIDQ2013571

Author name not available (Why is that?)

Publication date: 8 August 2017

Published in: (Search for Journal in Brave)

Abstract: In Turitsyn, Chertkov, Vucelja (2011) a non-reversible 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, Vucelja (2011). The scaling limit of LMH turns out to be a non-reversible piecewise deterministic exponentially ergodic `zig-zag' Markov process.

Full work available at URL: https://arxiv.org/abs/1509.00302

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: A piecewise deterministic scaling limit of lifted Metropolis-Hastings in the Curie-Weiss model

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2013571)