On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes (Q424499): Difference between revisions
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scientific article | scientific article; zbMATH DE number 6040302 | ||
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| Property / review text: Classical Cheeger inequalities for finite reversible Markov processes make a link between the spectral gap and the connectivity constants, which are obtained by minimizing isoperimetric-type quotients over decompositions of the state space into two disjoint parts. The purpose of the paper is to obtain such inequalities between the whole spectrum and decompositions of the state space into several parts, when the underlying graph is a cycle. Furthermore, the relation between an intermediate Dirichlet connectivity spectrum and the nodal domains of the eigenfunctions of the finite reversible Markov process under consideration is investigated. / rank | |||
| Property / review text | |||
Classical Cheeger inequalities for finite reversible Markov processes make a link between the spectral gap and the connectivity constants, which are obtained by minimizing isoperimetric-type quotients over decompositions of the state space into two disjoint parts. The purpose of the paper is to obtain such inequalities between the whole spectrum and decompositions of the state space into several parts, when the underlying graph is a cycle.NEWLINENEWLINE Furthermore, the relation between an intermediate Dirichlet connectivity spectrum and the nodal domains of the eigenfunctions of the finite reversible Markov process under consideration is investigated. | |||
| Property / review text: Classical Cheeger inequalities for finite reversible Markov processes make a link between the spectral gap and the connectivity constants, which are obtained by minimizing isoperimetric-type quotients over decompositions of the state space into two disjoint parts. The purpose of the paper is to obtain such inequalities between the whole spectrum and decompositions of the state space into several parts, when the underlying graph is a cycle.NEWLINENEWLINE Furthermore, the relation between an intermediate Dirichlet connectivity spectrum and the nodal domains of the eigenfunctions of the finite reversible Markov process under consideration is investigated. / rank | |||
Normal rank | |||
Latest revision as of 00:43, 28 June 2025
scientific article; zbMATH DE number 6040302
| Language | Label | Description | Also known as |
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| English | On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes |
scientific article; zbMATH DE number 6040302 |
Statements
On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes (English)
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1 June 2012
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reversible Markovian generator
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Cheeger's inequality
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Classical Cheeger inequalities for finite reversible Markov processes make a link between the spectral gap and the connectivity constants, which are obtained by minimizing isoperimetric-type quotients over decompositions of the state space into two disjoint parts. The purpose of the paper is to obtain such inequalities between the whole spectrum and decompositions of the state space into several parts, when the underlying graph is a cycle.NEWLINENEWLINE Furthermore, the relation between an intermediate Dirichlet connectivity spectrum and the nodal domains of the eigenfunctions of the finite reversible Markov process under consideration is investigated.
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