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Spectral Gap for Random-to-Random Shuffling on Linear Extensions

Ayyer, Arvind and Schilling, Anne and Thiery, Nicolas M (2017) Spectral Gap for Random-to-Random Shuffling on Linear Extensions. In: EXPERIMENTAL MATHEMATICS, 26 (1). pp. 22-30.

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Official URL: http://dx.doi.org/10.1080/10586458.2015.1107868

Abstract

In this article, we propose a new Markov chain which generalizes random-to-random shuffling on permutations to random-to-random shuffling on linear extensions of a finite poset of size n. We conjecture that the second largest eigenvalue of the transition matrix is bounded above by (1 + 1/n)(1 - 2/n) with equality when the poset is disconnected. This Markov chain provides a way to sample the linear extensions of the poset with a relaxation time bounded above by n(2)/(n + 2) and a mixing time of O(n(2)logn). We conjecture that the mixing time is in fact O(nlogn) as for the usual random-to-random shuffling.

Item Type: Journal Article
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Additional Information: Copy right for this article belongs to the TAYLOR & FRANCIS INC, 530 WALNUT STREET, STE 850, PHILADELPHIA, PA 19106 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 09 Mar 2017 05:01
Last Modified: 09 Mar 2017 05:01
URI: http://eprints.iisc.ernet.in/id/eprint/56332

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