Vicious walkers and random contraction matrices

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dc.creatorNovak, Jonathan
dc.date2007-05-07
dc.date2008-12-01
dc.date.accessioned2026-07-07T12:05:13Z
dc.date.available2026-07-07T12:05:13Z
dc.descriptionThe ensemble $\CUE^{(q)}$ of truncated random unitary matrices is a deformation of the usual Circular Unitary Ensemble depending on a discrete non-negative parameter $q.$ $\CUE^{(q)}$ is an exactly solved model of random contraction matrices originally introduced in the context of scattering theory. In this article, we exhibit a connection between $\CUE^{(q)}$ and Fisher's random-turns vicious walker model from statistical mechanics. In particular, we show that the moment generating function of the trace of a random matrix from $\CUE^{(q)}$ is a generating series for the partition function of Fisher's model, when the walkers are assumed to represent mutually attracting particles.
dc.description13 pages, 1 figures
dc.identifierhttps://arxiv.org/abs/0705.0984
dc.identifierhttp://arxiv.org/abs/0705.0984
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208318
dc.subjectCombinatorics
dc.subjectProbability
dc.subject05A16
dc.titleVicious walkers and random contraction matrices
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