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Published August 18, 2006 | public
Journal Article

Imaging geometry through dynamics: the observable representation


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.

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.

Additional details

August 19, 2023
October 19, 2023