Bootstrapping cascaded random matrix models: correlations in permutations of matrix products
Random matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through thick disordered media, as arises, for example, in optical scattering or electron transport, typicall...
| Main Authors: | , , |
|---|---|
| 其他作者: | |
| 格式: | Journal Article |
| 语言: | English |
| 出版: |
2024
|
| 主题: | |
| 在线阅读: | https://hdl.handle.net/10356/179433 |
| _version_ | 1826109993433169920 |
|---|---|
| author | Byrnes, Niall Greaves, Gary Royden Watson Foreman, Matthew R. |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Byrnes, Niall Greaves, Gary Royden Watson Foreman, Matthew R. |
| author_sort | Byrnes, Niall |
| collection | NTU |
| description | Random matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through thick disordered media, as arises, for example, in optical scattering or electron transport, typically necessitates cascading of multiple random matrices drawn from an underlying ensemble for thin media, greatly increasing the computational burden. Here we propose a dual pool based bootstrapping approach to speed up statistical studies of scattering in thick random media. We examine how potential matrix reuse in a pool based approach can impact statistical estimates of population averages. Specifically, we discuss how both bias and additional variance in the sample mean estimator are introduced through bootstrapping. In the diffusive scattering regime, the extra estimator variance is shown to originate from samples in which cascaded transfer matrices are permuted matrix products. Through analysis of the combinatorics and cycle structure of permutations we quantify the resulting correlations. Proofs of several analytic formulas enumerating the frequency with which correlations of different strengths occur are derived. Extension to the ballistic regime is briefly considered. |
| first_indexed | 2024-10-01T02:27:11Z |
| format | Journal Article |
| id | ntu-10356/179433 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:27:11Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-10356/1794332024-08-02T15:39:58Z Bootstrapping cascaded random matrix models: correlations in permutations of matrix products Byrnes, Niall Greaves, Gary Royden Watson Foreman, Matthew R. School of Electrical and Electronic Engineering School of Physical and Mathematical Sciences Institute for Digital Molecular Analytics and Science Mathematical Sciences Computation theory Electron transport properties Random matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through thick disordered media, as arises, for example, in optical scattering or electron transport, typically necessitates cascading of multiple random matrices drawn from an underlying ensemble for thin media, greatly increasing the computational burden. Here we propose a dual pool based bootstrapping approach to speed up statistical studies of scattering in thick random media. We examine how potential matrix reuse in a pool based approach can impact statistical estimates of population averages. Specifically, we discuss how both bias and additional variance in the sample mean estimator are introduced through bootstrapping. In the diffusive scattering regime, the extra estimator variance is shown to originate from samples in which cascaded transfer matrices are permuted matrix products. Through analysis of the combinatorics and cycle structure of permutations we quantify the resulting correlations. Proofs of several analytic formulas enumerating the frequency with which correlations of different strengths occur are derived. Extension to the ballistic regime is briefly considered. Ministry of Education (MOE) Nanyang Technological University Submitted/Accepted version NB was supported by Nanyang Technological University grant number SUG:022824-00001. GRWG was supported by the Singapore Ministry of Education Academic Research Fund (Tier 1); grant numbers: RG21/20 and RG23/20. MRF was supported by funding from the Institute for Digital Molecular Analytics and Science (IDMxS) under the Singapore Ministry of Education Research Centres of Excellence scheme. 2024-07-31T06:37:51Z 2024-07-31T06:37:51Z 2024 Journal Article Byrnes, N., Greaves, G. R. W. & Foreman, M. R. (2024). Bootstrapping cascaded random matrix models: correlations in permutations of matrix products. Physical Review E, 110(1), 015308-. https://dx.doi.org/10.1103/PhysRevE.110.015308 2470-0045 https://hdl.handle.net/10356/179433 10.1103/PhysRevE.110.015308 2-s2.0-85199414522 1 110 015308 en RG21/20 RG23/20 SUG022824-00001 Physical Review E © 2024 American Physical Society. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org//10.1103/PhysRevE.110.015308. application/pdf |
| spellingShingle | Mathematical Sciences Computation theory Electron transport properties Byrnes, Niall Greaves, Gary Royden Watson Foreman, Matthew R. Bootstrapping cascaded random matrix models: correlations in permutations of matrix products |
| title | Bootstrapping cascaded random matrix models: correlations in permutations of matrix products |
| title_full | Bootstrapping cascaded random matrix models: correlations in permutations of matrix products |
| title_fullStr | Bootstrapping cascaded random matrix models: correlations in permutations of matrix products |
| title_full_unstemmed | Bootstrapping cascaded random matrix models: correlations in permutations of matrix products |
| title_short | Bootstrapping cascaded random matrix models: correlations in permutations of matrix products |
| title_sort | bootstrapping cascaded random matrix models correlations in permutations of matrix products |
| topic | Mathematical Sciences Computation theory Electron transport properties |
| url | https://hdl.handle.net/10356/179433 |
| work_keys_str_mv | AT byrnesniall bootstrappingcascadedrandommatrixmodelscorrelationsinpermutationsofmatrixproducts AT greavesgaryroydenwatson bootstrappingcascadedrandommatrixmodelscorrelationsinpermutationsofmatrixproducts AT foremanmatthewr bootstrappingcascadedrandommatrixmodelscorrelationsinpermutationsofmatrixproducts |