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Full current statistics for a disordered open exclusion process

Ayyer, Arvind (2016) Full current statistics for a disordered open exclusion process. In: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 49 (15).

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Official URL: http://dx.doi.org/10.1088/1751-8113/49/15/155003


We consider the nonabelian sandpile model defined on directed trees by Ayyer et al. (2015 Commun. Math. Phys. 335 1065). and restrict it to the special case of a one-dimensional lattice of n sites which has open boundaries and disordered hopping rates. We focus on the joint distribution of the integrated currents across each bond simultaneously, and calculate its cumulant generating function exactly. Surprisingly, the process conditioned on seeing specified currents across each bond turns out to be a renormalised version of the same process. We also remark on a duality property of the large deviation function. Lastly, all eigenvalues and both Perron eigenvectors of the tilted generator are determined.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the IOP PUBLISHING LTD, TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND
Keywords: nonequilibrium process; current fluctuations; large deviation function; modified Doob transform
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 07 Apr 2016 05:18
Last Modified: 07 Apr 2016 05:18
URI: http://eprints.iisc.ac.in/id/eprint/53603

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