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The band structure of a model of spatial random permutation

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The band structure of a model of spatial random permutation. / Fyodorov, Yan; Muirhead, Stephen.

In: PROBABILITY THEORY AND RELATED FIELDS, Vol. 179, No. 3-4, 07.02.2021, p. 543-587.

Research output: Contribution to journalArticlepeer-review

Harvard

Fyodorov, Y & Muirhead, S 2021, 'The band structure of a model of spatial random permutation', PROBABILITY THEORY AND RELATED FIELDS, vol. 179, no. 3-4, pp. 543-587. https://doi.org/10.1007/s00440-020-01019-z

APA

Fyodorov, Y., & Muirhead, S. (2021). The band structure of a model of spatial random permutation. PROBABILITY THEORY AND RELATED FIELDS, 179(3-4), 543-587. https://doi.org/10.1007/s00440-020-01019-z

Vancouver

Fyodorov Y, Muirhead S. The band structure of a model of spatial random permutation. PROBABILITY THEORY AND RELATED FIELDS. 2021 Feb 7;179(3-4):543-587. https://doi.org/10.1007/s00440-020-01019-z

Author

Fyodorov, Yan ; Muirhead, Stephen. / The band structure of a model of spatial random permutation. In: PROBABILITY THEORY AND RELATED FIELDS. 2021 ; Vol. 179, No. 3-4. pp. 543-587.

Bibtex Download

@article{d653046756c04fa8ad9e6b19c0e8777f,
title = "The band structure of a model of spatial random permutation",
abstract = "We study a random permutation of a lattice box in which each permutation is given a Boltzmann weight with energy equal to the total Euclidean displacement. Our main result establishes the band structure of the model as the box-size N tends to infinity and the inverse temperature β tends to zero; in particular, we show that the mean displacement is of order min { 1 / β, N}. In one dimension our results are more precise, specifying leading-order constants and giving bounds on the rates of convergence. Our proofs exploit a connection, via matrix permanents, between random permutations and Gaussian fields; although this connection is well-known in other settings, to the best of our knowledge its application to the study of random permutations is novel. As a byproduct of our analysis, we also provide asymptotics for the permanents of Kac–Murdock–Szeg{\H o} matrices.",
author = "Yan Fyodorov and Stephen Muirhead",
note = "Funding Information: This research was supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant EP/N009436/1 “The many faces of random characteristic polynomials” and the Australian Research Council (ARC) Discovery Early Career Researcher Award DE200101467. The authors would like to thank Jeremiah Buckley, Naomi Feldheim and Daniel Ueltschi for enlightening discussions, and in particular Ron Peled for helpful discussions at an early stage. The authors would also like to thank an anonymous referee for detailed comments which improved the presentation of the paper, and also for pointing out corrections to an earlier version. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = feb,
day = "7",
doi = "10.1007/s00440-020-01019-z",
language = "English",
volume = "179",
pages = "543--587",
journal = "PROBABILITY THEORY AND RELATED FIELDS",
issn = "0178-8051",
publisher = "Springer New York",
number = "3-4",

}

RIS (suitable for import to EndNote) Download

TY - JOUR

T1 - The band structure of a model of spatial random permutation

AU - Fyodorov, Yan

AU - Muirhead, Stephen

N1 - Funding Information: This research was supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant EP/N009436/1 “The many faces of random characteristic polynomials” and the Australian Research Council (ARC) Discovery Early Career Researcher Award DE200101467. The authors would like to thank Jeremiah Buckley, Naomi Feldheim and Daniel Ueltschi for enlightening discussions, and in particular Ron Peled for helpful discussions at an early stage. The authors would also like to thank an anonymous referee for detailed comments which improved the presentation of the paper, and also for pointing out corrections to an earlier version. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/2/7

Y1 - 2021/2/7

N2 - We study a random permutation of a lattice box in which each permutation is given a Boltzmann weight with energy equal to the total Euclidean displacement. Our main result establishes the band structure of the model as the box-size N tends to infinity and the inverse temperature β tends to zero; in particular, we show that the mean displacement is of order min { 1 / β, N}. In one dimension our results are more precise, specifying leading-order constants and giving bounds on the rates of convergence. Our proofs exploit a connection, via matrix permanents, between random permutations and Gaussian fields; although this connection is well-known in other settings, to the best of our knowledge its application to the study of random permutations is novel. As a byproduct of our analysis, we also provide asymptotics for the permanents of Kac–Murdock–Szegő matrices.

AB - We study a random permutation of a lattice box in which each permutation is given a Boltzmann weight with energy equal to the total Euclidean displacement. Our main result establishes the band structure of the model as the box-size N tends to infinity and the inverse temperature β tends to zero; in particular, we show that the mean displacement is of order min { 1 / β, N}. In one dimension our results are more precise, specifying leading-order constants and giving bounds on the rates of convergence. Our proofs exploit a connection, via matrix permanents, between random permutations and Gaussian fields; although this connection is well-known in other settings, to the best of our knowledge its application to the study of random permutations is novel. As a byproduct of our analysis, we also provide asymptotics for the permanents of Kac–Murdock–Szegő matrices.

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U2 - 10.1007/s00440-020-01019-z

DO - 10.1007/s00440-020-01019-z

M3 - Article

VL - 179

SP - 543

EP - 587

JO - PROBABILITY THEORY AND RELATED FIELDS

JF - PROBABILITY THEORY AND RELATED FIELDS

SN - 0178-8051

IS - 3-4

ER -

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