Glauber dynamics on hyperbolic graphs : boundary conditions and mixing time
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1281 | |
dc.contributor.author | Bianchi, Alessandra | |
dc.date.accessioned | 2016-03-24T17:38:20Z | |
dc.date.available | 2019-06-28T08:02:54Z | |
dc.date.issued | 2007 | |
dc.description.abstract | We study a continuous time Glauber dynamics reversible with respect to the Ising model on hyperbolic graphs and analyze the effect of boundary conditions on the mixing time. Specifically, we consider the dynamics on an $n$-vertex ball of the hyperbolic graph $H(v,s)$, where $v$ is the number of neighbors of each vertex and $s$ is the number of sides of each face, conditioned on having $(+)$-boundary. If $v>4$, $s>3$ and for all low enough temperatures (phase coexistence region) we prove that the spectral gap of this dynamics is bounded below by a constant independent of $n$. This implies that the mixing time grows at most linearly in $n$, in contrast to the free boundary case where it is polynomial with exponent growing with the inverse temperature $b$. Such a result extends to hyperbolic graphs the work done by Martinelli, Sinclair and Weitz for the analogous system on regular tree graphs, and provides a further example of influence of the boundary condition on the mixing time. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/2421 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/1940 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Ising model | eng |
dc.subject.other | Glauber dynamics | eng |
dc.subject.other | hyperbolic graphs | eng |
dc.subject.other | Dirichlet form | eng |
dc.subject.other | spectral gap | eng |
dc.subject.other | mixing time | eng |
dc.title | Glauber dynamics on hyperbolic graphs : boundary conditions and mixing time | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- 558793894.pdf
- Size:
- 394.41 KB
- Format:
- Adobe Portable Document Format
- Description: