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Loop-Erased Walks and Random Matrices

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Loop-Erased Walks and Random Matrices. / Arista, Jonas; O’Connell, Neil.
In: Journal of Statistical Physics, Vol. 177, No. 3, 06.11.2019, p. 528-567.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Arista, J & O’Connell, N 2019, 'Loop-Erased Walks and Random Matrices', Journal of Statistical Physics, vol. 177, no. 3, pp. 528-567. https://doi.org/10.1007/s10955-019-02378-1

APA

Arista, J., & O’Connell, N. (2019). Loop-Erased Walks and Random Matrices. Journal of Statistical Physics, 177(3), 528-567. https://doi.org/10.1007/s10955-019-02378-1

Vancouver

Arista J, O’Connell N. Loop-Erased Walks and Random Matrices. Journal of Statistical Physics. 2019 Nov 6;177(3):528-567. doi: 10.1007/s10955-019-02378-1

Author

Arista, Jonas ; O’Connell, Neil. / Loop-Erased Walks and Random Matrices. In: Journal of Statistical Physics. 2019 ; Vol. 177, No. 3. pp. 528-567.

Bibtex

@article{d6419259a8174620b657102da87e933f,
title = "Loop-Erased Walks and Random Matrices",
abstract = "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.",
author = "Jonas Arista and Neil O{\textquoteright}Connell",
year = "2019",
month = nov,
day = "6",
doi = "10.1007/s10955-019-02378-1",
language = "English",
volume = "177",
pages = "528--567",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "3",

}

RIS

TY - JOUR

T1 - Loop-Erased Walks and Random Matrices

AU - Arista, Jonas

AU - O’Connell, Neil

PY - 2019/11/6

Y1 - 2019/11/6

N2 - 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.

AB - 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.

U2 - 10.1007/s10955-019-02378-1

DO - 10.1007/s10955-019-02378-1

M3 - Journal article

C2 - 31708593

VL - 177

SP - 528

EP - 567

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3

ER -