Laplacians on Infinite Graphs
The main focus in this memoir is on Laplacians on both weighted graphs and weighted metric graphs. Let us emphasize that we consider infinite locally finite graphs and do not make any further geometric assumptions. Whereas the existing literature usually treats these two types of Laplacian operators...
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European Mathematical Society Publishing House
2022
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=3808241&site=ehost-live header: @attributes: shortDbName: nlebk uiTerm: 3808241 longDbName: eBook Collection (EBSCOhost) uiTag: AN controlInfo: bkinfo: btl: Laplacians on Infinite Graphs aug: au: Aleksey Kostenko Noema Nicolussi sertl: Memoirs of the European Mathematical Society isbn: 9783985470259 9783985475254 imageinfo: pubinfo: dt: @attributes: year: 2022 month: 01 day: 01 dtAvail: @attributes: year: 2024 month: 05 day: 03 vid: 00003 pub: European Mathematical Society Publishing House pubContract: European Mathematical Society - EMS - Publishing House GmbH place: Berlin price: 0.01 limitsGroup: maxCheckoutDays: 1500 pda: N printPagesOffline: 100 printPagesOnline: 100 previewPages: 10000 prePubGroup: dewey: @attributes: class: 511.5 item: 511 .5 lc: @attributes: class: QA166 item: QA 166 artinfo: ui: 3808241 1378642006 formats: fmt: @attributes: type: EB doid: NL$3808241$PDF caption: PDF download: Y tig: atl: Laplacians on Infinite Graphs ptl: Laplacians on Infinite Graphs aug: au: Aleksey Kostenko Noema Nicolussi su: Laplacian matrices Markov spectrum sug: subj: MATHEMATICS / Graphic Methods MATHEMATICS / Infinity Laplacian matrices Markov spectrum ab: The main focus in this memoir is on Laplacians on both weighted graphs and weighted metric graphs. Let us emphasize that we consider infinite locally finite graphs and do not make any further geometric assumptions. Whereas the existing literature usually treats these two types of Laplacian operators separately, we approach them in a uniform manner in the present work and put particular emphasis on the relationship between them. One of our main conceptual messages is that these two settings should be regarded as complementary (rather than opposite) and exactly their interplay leads to important further insight on both sides. Our central goal is twofold. First of all, we explore the relationships between these two objects by comparing their basic spectral (self-adjointness, spectral gap, etc.), parabolic (Markovian uniqueness, recurrence, stochastic completeness, etc.), and metric (quasi isometries, intrinsic metrics, etc.) properties. In turn, we exploit these connections either to prove new results for Laplacians on metric graphs or to provide new proofs and perspective on the recent progress in weighted graph Laplacians. We also demonstrate our findings by considering several important classes of graphs (Cayley graphs, tessellations, and antitrees). pubtype: eBook doctype: Book ougenre: Book language: English copyright: @attributes: flag: N copyrightText: holdings: @attributes: islocal: N |
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