Eigenvalue spectrum of transition matrix of dual Sierpinski gaskets and its applications

The eigenvalue spectrum of the transition matrix of a network contains much information about its structural properties and is related to the behavior of various dynamical processes performed on it. In this paper, we study the eigenvalues of the transition matrix of the dual Sierpinski gaskets embed...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-08, Vol.45 (34), p.345101-1-345101-11
Main Authors: Wu, Shunqi, Zhang, Zhongzhi
Format: Article
Language:English
Subjects:
Eigenvalues
Exact sciences and technology
Fractal analysis
Fractals
Gaskets
Graph theory
Mathematical analysis
Networks
Physics
Random walk
Spectra
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c361t-86344f017dfe6b3069e5cd68592608ea890980faacda63c7ca4c5a62c64d59353
cites cdi_FETCH-LOGICAL-c361t-86344f017dfe6b3069e5cd68592608ea890980faacda63c7ca4c5a62c64d59353
container_end_page 1-345101-11
container_issue 34
container_start_page 345101
container_title Journal of physics. A, Mathematical and theoretical
container_volume 45
creator Wu, Shunqi
Zhang, Zhongzhi
description The eigenvalue spectrum of the transition matrix of a network contains much information about its structural properties and is related to the behavior of various dynamical processes performed on it. In this paper, we study the eigenvalues of the transition matrix of the dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces. We obtain all the eigenvalues, as well as their corresponding degeneracies, by making use of the spectral decimation technique. We then apply the obtained eigenvalues to determine the exact number of spanning trees in the studied fractals and derive an explicit formula of the eigentime identity for random walks taking place on them.
doi_str_mv 10.1088/1751-8113/45/34/345101
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1669859085</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1669859085</sourcerecordid><originalsourceid>FETCH-LOGICAL-c361t-86344f017dfe6b3069e5cd68592608ea890980faacda63c7ca4c5a62c64d59353</originalsourceid><addsrcrecordid>eNqFkFtLAzEQhYMoWKt_QfIi-LI22VyafZRSL1DwQQXfwpjNlrR7M7Mr-u_dZUtfhYEZknPOMB8h15zdcWbMgi8VTwznYiHVQsihFGf8hMwOHyk_Pc5cnJMLxB1jSrIsnZGPddj6-hvK3lNsvetiX9GmoF2EGkMXmppW0MXwMz7mPZT0NfjYhhr3gW4B975DCnVOw9jbtgwORhdekrMCSvRXhz4n7w_rt9VTsnl5fF7dbxInNO8So4WUBePLvPD6UzCdeeVybVSWamY8mIxlhhUALgct3NKBdAp06rTMVSaUmJPbKbeNzVfvsbNVQOfLEmrf9Gi51tmQxswo1ZPUxQYx-sK2MVQQfy1ndkRpR0p2pGSlskLaCeVgvDnsAHRQFgMbF_DoTocblJDZoEsnXWhau2v6WA-X_xf-B6dxg0M</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1669859085</pqid></control><display><type>article</type><title>Eigenvalue spectrum of transition matrix of dual Sierpinski gaskets and its applications</title><source>Institute of Physics:Jisc Collections:IOP Publishing Read and Publish 2024-2025 (Reading List)</source><creator>Wu, Shunqi ; Zhang, Zhongzhi</creator><creatorcontrib>Wu, Shunqi ; Zhang, Zhongzhi</creatorcontrib><description>The eigenvalue spectrum of the transition matrix of a network contains much information about its structural properties and is related to the behavior of various dynamical processes performed on it. In this paper, we study the eigenvalues of the transition matrix of the dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces. We obtain all the eigenvalues, as well as their corresponding degeneracies, by making use of the spectral decimation technique. We then apply the obtained eigenvalues to determine the exact number of spanning trees in the studied fractals and derive an explicit formula of the eigentime identity for random walks taking place on them.</description><identifier>ISSN: 1751-8113</identifier><identifier>EISSN: 1751-8121</identifier><identifier>DOI: 10.1088/1751-8113/45/34/345101</identifier><identifier>CODEN: JPHAC5</identifier><language>eng</language><publisher>Bristol: IOP Publishing</publisher><subject>Eigenvalues ; Exact sciences and technology ; Fractal analysis ; Fractals ; Gaskets ; Graph theory ; Mathematical analysis ; Networks ; Physics ; Random walk ; Spectra</subject><ispartof>Journal of physics. A, Mathematical and theoretical, 2012-08, Vol.45 (34), p.345101-1-345101-11</ispartof><rights>2012 IOP Publishing Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c361t-86344f017dfe6b3069e5cd68592608ea890980faacda63c7ca4c5a62c64d59353</citedby><cites>FETCH-LOGICAL-c361t-86344f017dfe6b3069e5cd68592608ea890980faacda63c7ca4c5a62c64d59353</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=26345349$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Wu, Shunqi</creatorcontrib><creatorcontrib>Zhang, Zhongzhi</creatorcontrib><title>Eigenvalue spectrum of transition matrix of dual Sierpinski gaskets and its applications</title><title>Journal of physics. A, Mathematical and theoretical</title><addtitle>JPhysA</addtitle><addtitle>J. Phys. A: Math. Theor</addtitle><description>The eigenvalue spectrum of the transition matrix of a network contains much information about its structural properties and is related to the behavior of various dynamical processes performed on it. In this paper, we study the eigenvalues of the transition matrix of the dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces. We obtain all the eigenvalues, as well as their corresponding degeneracies, by making use of the spectral decimation technique. We then apply the obtained eigenvalues to determine the exact number of spanning trees in the studied fractals and derive an explicit formula of the eigentime identity for random walks taking place on them.</description><subject>Eigenvalues</subject><subject>Exact sciences and technology</subject><subject>Fractal analysis</subject><subject>Fractals</subject><subject>Gaskets</subject><subject>Graph theory</subject><subject>Mathematical analysis</subject><subject>Networks</subject><subject>Physics</subject><subject>Random walk</subject><subject>Spectra</subject><issn>1751-8113</issn><issn>1751-8121</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNqFkFtLAzEQhYMoWKt_QfIi-LI22VyafZRSL1DwQQXfwpjNlrR7M7Mr-u_dZUtfhYEZknPOMB8h15zdcWbMgi8VTwznYiHVQsihFGf8hMwOHyk_Pc5cnJMLxB1jSrIsnZGPddj6-hvK3lNsvetiX9GmoF2EGkMXmppW0MXwMz7mPZT0NfjYhhr3gW4B975DCnVOw9jbtgwORhdekrMCSvRXhz4n7w_rt9VTsnl5fF7dbxInNO8So4WUBePLvPD6UzCdeeVybVSWamY8mIxlhhUALgct3NKBdAp06rTMVSaUmJPbKbeNzVfvsbNVQOfLEmrf9Gi51tmQxswo1ZPUxQYx-sK2MVQQfy1ndkRpR0p2pGSlskLaCeVgvDnsAHRQFgMbF_DoTocblJDZoEsnXWhau2v6WA-X_xf-B6dxg0M</recordid><startdate>20120831</startdate><enddate>20120831</enddate><creator>Wu, Shunqi</creator><creator>Zhang, Zhongzhi</creator><general>IOP Publishing</general><general>IOP</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20120831</creationdate><title>Eigenvalue spectrum of transition matrix of dual Sierpinski gaskets and its applications</title><author>Wu, Shunqi ; Zhang, Zhongzhi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c361t-86344f017dfe6b3069e5cd68592608ea890980faacda63c7ca4c5a62c64d59353</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Eigenvalues</topic><topic>Exact sciences and technology</topic><topic>Fractal analysis</topic><topic>Fractals</topic><topic>Gaskets</topic><topic>Graph theory</topic><topic>Mathematical analysis</topic><topic>Networks</topic><topic>Physics</topic><topic>Random walk</topic><topic>Spectra</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wu, Shunqi</creatorcontrib><creatorcontrib>Zhang, Zhongzhi</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of physics. A, Mathematical and theoretical</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wu, Shunqi</au><au>Zhang, Zhongzhi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Eigenvalue spectrum of transition matrix of dual Sierpinski gaskets and its applications</atitle><jtitle>Journal of physics. A, Mathematical and theoretical</jtitle><stitle>JPhysA</stitle><addtitle>J. Phys. A: Math. Theor</addtitle><date>2012-08-31</date><risdate>2012</risdate><volume>45</volume><issue>34</issue><spage>345101</spage><epage>1-345101-11</epage><pages>345101-1-345101-11</pages><issn>1751-8113</issn><eissn>1751-8121</eissn><coden>JPHAC5</coden><abstract>The eigenvalue spectrum of the transition matrix of a network contains much information about its structural properties and is related to the behavior of various dynamical processes performed on it. In this paper, we study the eigenvalues of the transition matrix of the dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces. We obtain all the eigenvalues, as well as their corresponding degeneracies, by making use of the spectral decimation technique. We then apply the obtained eigenvalues to determine the exact number of spanning trees in the studied fractals and derive an explicit formula of the eigentime identity for random walks taking place on them.</abstract><cop>Bristol</cop><pub>IOP Publishing</pub><doi>10.1088/1751-8113/45/34/345101</doi><tpages>11</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1751-8113
ispartof Journal of physics. A, Mathematical and theoretical, 2012-08, Vol.45 (34), p.345101-1-345101-11
issn 1751-8113
1751-8121
language eng
recordid cdi_proquest_miscellaneous_1669859085
source Institute of Physics:Jisc Collections:IOP Publishing Read and Publish 2024-2025 (Reading List)
subjects Eigenvalues
Exact sciences and technology
Fractal analysis
Fractals
Gaskets
Graph theory
Mathematical analysis
Networks
Physics
Random walk
Spectra
title Eigenvalue spectrum of transition matrix of dual Sierpinski gaskets and its applications
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-31T06%3A58%3A47IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Eigenvalue%20spectrum%20of%20transition%20matrix%20of%20dual%20Sierpinski%20gaskets%20and%20its%20applications&rft.jtitle=Journal%20of%20physics.%20A,%20Mathematical%20and%20theoretical&rft.au=Wu,%20Shunqi&rft.date=2012-08-31&rft.volume=45&rft.issue=34&rft.spage=345101&rft.epage=1-345101-11&rft.pages=345101-1-345101-11&rft.issn=1751-8113&rft.eissn=1751-8121&rft.coden=JPHAC5&rft_id=info:doi/10.1088/1751-8113/45/34/345101&rft_dat=%3Cproquest_cross%3E1669859085%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c361t-86344f017dfe6b3069e5cd68592608ea890980faacda63c7ca4c5a62c64d59353%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1669859085&rft_id=info:pmid/&rfr_iscdi=true