A note on weak convergence results for uniform infinite causal triangulations
We discuss uniform infinite causal triangulations and equivalence to the size biased branching process measure - the critical Galton-Watson branching process distribution conditioned on non-extinction. Using known results from the theory of branching processes, this relation is used to prove weak co...
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| Format: | Journal article |
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2011
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| _version_ | 1826283308787433472 |
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| author | Sisko, V Yambartsev, A Zohren, S |
| author_facet | Sisko, V Yambartsev, A Zohren, S |
| author_sort | Sisko, V |
| collection | OXFORD |
| description | We discuss uniform infinite causal triangulations and equivalence to the size biased branching process measure - the critical Galton-Watson branching process distribution conditioned on non-extinction. Using known results from the theory of branching processes, this relation is used to prove weak convergence of the joint length-area process of a uniform infinite causal triangulations to a limiting diffusion. The diffusion equation enables us to determine the physical Hamiltonian and Green's function from the Feynman-Kac procedure, providing us with a mathematical rigorous proof of certain scaling limits of causal dynamical triangulations. |
| first_indexed | 2024-03-07T00:56:58Z |
| format | Journal article |
| id | oxford-uuid:88699570-a4d6-487b-9616-2951e866b45e |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:56:58Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:88699570-a4d6-487b-9616-2951e866b45e2022-03-26T22:17:04ZA note on weak convergence results for uniform infinite causal triangulationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:88699570-a4d6-487b-9616-2951e866b45eSymplectic Elements at Oxford2011Sisko, VYambartsev, AZohren, SWe discuss uniform infinite causal triangulations and equivalence to the size biased branching process measure - the critical Galton-Watson branching process distribution conditioned on non-extinction. Using known results from the theory of branching processes, this relation is used to prove weak convergence of the joint length-area process of a uniform infinite causal triangulations to a limiting diffusion. The diffusion equation enables us to determine the physical Hamiltonian and Green's function from the Feynman-Kac procedure, providing us with a mathematical rigorous proof of certain scaling limits of causal dynamical triangulations. |
| spellingShingle | Sisko, V Yambartsev, A Zohren, S A note on weak convergence results for uniform infinite causal triangulations |
| title | A note on weak convergence results for uniform infinite causal
triangulations |
| title_full | A note on weak convergence results for uniform infinite causal
triangulations |
| title_fullStr | A note on weak convergence results for uniform infinite causal
triangulations |
| title_full_unstemmed | A note on weak convergence results for uniform infinite causal
triangulations |
| title_short | A note on weak convergence results for uniform infinite causal
triangulations |
| title_sort | note on weak convergence results for uniform infinite causal triangulations |
| work_keys_str_mv | AT siskov anoteonweakconvergenceresultsforuniforminfinitecausaltriangulations AT yambartseva anoteonweakconvergenceresultsforuniforminfinitecausaltriangulations AT zohrens anoteonweakconvergenceresultsforuniforminfinitecausaltriangulations AT siskov noteonweakconvergenceresultsforuniforminfinitecausaltriangulations AT yambartseva noteonweakconvergenceresultsforuniforminfinitecausaltriangulations AT zohrens noteonweakconvergenceresultsforuniforminfinitecausaltriangulations |