Computing growth rates of random matrix products via generating functions
Abstract Random matrix products arise in many science and engineering problems. An efficient evaluation of its growth rate is of great interest to researchers in diverse fields. In the current paper, we reformulate this problem with a generating function approach, based on which two analytic methods...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer
2022-09-01
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| Series: | AAPPS Bulletin |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/s43673-022-00057-0 |
| _version_ | 1811208729361645568 |
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| author | Naranmandula Bao Junbiao Lu Ruobing Cai Yueheng Lan |
| author_facet | Naranmandula Bao Junbiao Lu Ruobing Cai Yueheng Lan |
| author_sort | Naranmandula Bao |
| collection | DOAJ |
| description | Abstract Random matrix products arise in many science and engineering problems. An efficient evaluation of its growth rate is of great interest to researchers in diverse fields. In the current paper, we reformulate this problem with a generating function approach, based on which two analytic methods are proposed to compute the growth rate. The new formalism is demonstrated in a series of examples including an Ising model subject to on-site random magnetic fields, which seems very efficient and easy to implement. Through an extensive comparison with numerical computation, we see that the analytic results are valid in a region of considerable size.The formulation could be conveniently applied to stochastic processes with more complex structures. |
| first_indexed | 2024-04-12T04:26:31Z |
| format | Article |
| id | doaj.art-3406ae80870c486386a28ee3a1f31379 |
| institution | Directory Open Access Journal |
| issn | 2309-4710 |
| language | English |
| last_indexed | 2024-04-12T04:26:31Z |
| publishDate | 2022-09-01 |
| publisher | Springer |
| record_format | Article |
| series | AAPPS Bulletin |
| spelling | doaj.art-3406ae80870c486386a28ee3a1f313792022-12-22T03:48:04ZengSpringerAAPPS Bulletin2309-47102022-09-0132111110.1007/s43673-022-00057-0Computing growth rates of random matrix products via generating functionsNaranmandula Bao0Junbiao Lu1Ruobing Cai2Yueheng Lan3College of Physics and Electronics Information, Inner Mongolian University for NationalitiesSchool of Science, Beijing University of Posts and TelecommunicationsSchool of Science, Beijing University of Posts and TelecommunicationsSchool of Science, Beijing University of Posts and TelecommunicationsAbstract Random matrix products arise in many science and engineering problems. An efficient evaluation of its growth rate is of great interest to researchers in diverse fields. In the current paper, we reformulate this problem with a generating function approach, based on which two analytic methods are proposed to compute the growth rate. The new formalism is demonstrated in a series of examples including an Ising model subject to on-site random magnetic fields, which seems very efficient and easy to implement. Through an extensive comparison with numerical computation, we see that the analytic results are valid in a region of considerable size.The formulation could be conveniently applied to stochastic processes with more complex structures.https://doi.org/10.1007/s43673-022-00057-0Lyapunov exponentRandom sequenceGenerating functionInvariant polynomialMatrix products |
| spellingShingle | Naranmandula Bao Junbiao Lu Ruobing Cai Yueheng Lan Computing growth rates of random matrix products via generating functions AAPPS Bulletin Lyapunov exponent Random sequence Generating function Invariant polynomial Matrix products |
| title | Computing growth rates of random matrix products via generating functions |
| title_full | Computing growth rates of random matrix products via generating functions |
| title_fullStr | Computing growth rates of random matrix products via generating functions |
| title_full_unstemmed | Computing growth rates of random matrix products via generating functions |
| title_short | Computing growth rates of random matrix products via generating functions |
| title_sort | computing growth rates of random matrix products via generating functions |
| topic | Lyapunov exponent Random sequence Generating function Invariant polynomial Matrix products |
| url | https://doi.org/10.1007/s43673-022-00057-0 |
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