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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. http://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.


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http://dx.doi.org/10.1088/0305-4470/39/33/004DOIUNSPECIFIED
http://www.iop.org/EJ/abstract/0305-4470/39/33/004/PublisherUNSPECIFIED
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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.
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Record Number:CaltechAUTHORS:20090917-133724756
Persistent URL:http://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
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15920
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:05 Oct 2009 17:58
Last Modified:26 Dec 2012 11:23

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