| O'Connell's process as a vicious Brownian motion. | |
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MedLine Citation:
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PMID: 22304077 Owner: NLM Status: Publisher |
Abstract/OtherAbstract:
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Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of the quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever. |
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Authors:
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Makoto Katori |
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Publication Detail:
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Type: JOURNAL ARTICLE Date: 2011-12-27 |
Journal Detail:
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Title: Physical review. E, Statistical, nonlinear, and soft matter physics Volume: 84 ISSN: 1550-2376 ISO Abbreviation: - Publication Date: 2011 Dec |
Date Detail:
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Created Date: 2012-2-6 Completed Date: - Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 101136452 Medline TA: Phys Rev E Stat Nonlin Soft Matter Phys Country: - |
Other Details:
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Languages: ENG Pagination: 061144 Citation Subset: - |
Affiliation:
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Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan. |
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