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Loop-Erased Walks and Random Matrices

It is well known that there are close connections between non-intersecting processes in one dimension and random matrices, based on the reflection principle. There is a generalisation of the reflection principle for more general (e.g. planar) processes, due to Fomin, in which the non-intersection co...

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Detalles Bibliográficos
Autores principales: Arista, Jonas, O’Connell, Neil
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6825037/
https://www.ncbi.nlm.nih.gov/pubmed/31708593
http://dx.doi.org/10.1007/s10955-019-02378-1
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author Arista, Jonas
O’Connell, Neil
author_facet Arista, Jonas
O’Connell, Neil
author_sort Arista, Jonas
collection PubMed
description It is well known that there are close connections between non-intersecting processes in one dimension and random matrices, based on the reflection principle. There is a generalisation of the reflection principle for more general (e.g. planar) processes, due to Fomin, in which the non-intersection condition is replaced by a condition involving loop-erased paths. In the context of independent Brownian motions in suitable planar domains, this also has close connections to random matrices. An example of this was first observed by Sato and Katori (Phys Rev E 83:041127, 2011). We present further examples which give rise to various Cauchy-type ensembles. We also extend Fomin’s identity to the affine setting and show that in this case, by considering independent Brownian motions in an annulus, one obtains a novel interpretation of the circular orthogonal ensemble.
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spelling pubmed-68250372019-11-06 Loop-Erased Walks and Random Matrices Arista, Jonas O’Connell, Neil J Stat Phys Article It is well known that there are close connections between non-intersecting processes in one dimension and random matrices, based on the reflection principle. There is a generalisation of the reflection principle for more general (e.g. planar) processes, due to Fomin, in which the non-intersection condition is replaced by a condition involving loop-erased paths. In the context of independent Brownian motions in suitable planar domains, this also has close connections to random matrices. An example of this was first observed by Sato and Katori (Phys Rev E 83:041127, 2011). We present further examples which give rise to various Cauchy-type ensembles. We also extend Fomin’s identity to the affine setting and show that in this case, by considering independent Brownian motions in an annulus, one obtains a novel interpretation of the circular orthogonal ensemble. Springer US 2019-09-06 2019 /pmc/articles/PMC6825037/ /pubmed/31708593 http://dx.doi.org/10.1007/s10955-019-02378-1 Text en © The Author(s) 2019 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Arista, Jonas
O’Connell, Neil
Loop-Erased Walks and Random Matrices
title Loop-Erased Walks and Random Matrices
title_full Loop-Erased Walks and Random Matrices
title_fullStr Loop-Erased Walks and Random Matrices
title_full_unstemmed Loop-Erased Walks and Random Matrices
title_short Loop-Erased Walks and Random Matrices
title_sort loop-erased walks and random matrices
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6825037/
https://www.ncbi.nlm.nih.gov/pubmed/31708593
http://dx.doi.org/10.1007/s10955-019-02378-1
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