Imaging geometry through dynamics: the observable representation

Gaveau, Bernard and Schulman, Lawrence S. and Schulman, Leonard J. (2006) Imaging geometry through dynamics: the observable representation. Journal of Physics A: Mathematical and General, 39 (33). pp. 10307-10321. ISSN 0305-4470. doi:10.1088/0305-4470/39/33/004. https://resolver.caltech.edu/CaltechAUTHORS:20090917-133724756

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Abstract

For many stochastic processes there is an underlying coordinate space, V, with the process moving from point to point in V or on variables (such as spin configurations) defined with respect to V. There is a matrix of transition probabilities (whether between points in V or between variables defined on V) and we focus on its 'slow' eigenvectors, those with eigenvalues closest to that of the stationary eigenvector. These eigenvectors are the 'observables', and can be used to recover geometrical features of V.

Item Type:

Article

Related URLs:

URL	URL Type	Description
http://dx.doi.org/10.1088/0305-4470/39/33/004	DOI	UNSPECIFIED
http://www.iop.org/EJ/abstract/0305-4470/39/33/004/	Publisher	UNSPECIFIED
http://stacks.iop.org/JPhysA/39/10307	Publisher	UNSPECIFIED

ORCID:

Author	ORCID
Schulman, Lawrence S.	0000-0001-5715-0542
Schulman, Leonard J.	0000-0001-9901-2797

Additional Information:

Copyright © Institute of Physics and IOP Publishing Limited 2006. Received 25 March 2006, in final form 5 June 2006. Published 2 August 2006. Print publication: Issue 33 (18 August 2006). We thank Bertrand Duplantier, Thomas Gilbert, Peter Greiner, Annick Lesne and Jean-Marc Luck for helpful discussions. This work was supported in part by NSF, NSA and ARO grants.

Funders:

Funding Agency	Grant Number
NSF	UNSPECIFIED
National Security Agency	UNSPECIFIED
Army Research Office	UNSPECIFIED

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DOI:

10.1088/0305-4470/39/33/004

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CaltechAUTHORS:20090917-133724756

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20090917-133724756

Official Citation:

Imaging geometry through dynamics: the observable representation Bernard Gaveau, Lawrence S Schulman and Leonard J Schulman 2006 J. Phys. A: Math. Gen. 39 10307-10321 doi: 10.1088/0305-4470/39/33/004

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ID Code:

15920

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CaltechAUTHORS

Deposited By:

George Porter

Deposited On:

05 Oct 2009 17:58

Last Modified:

12 Jul 2022 19:47

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