Título:
Scaling limits and generic bounds for exploration processes
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Autor:
Bermolen, Paola
Jonckheere, Matthieu
Sanders, Jaron
Jonckheere, Matthieu
Sanders, Jaron
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Tipo de documento:
Preprint
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Palabras clave:
Random sequential adsorption
Random graphs
Scaling limits
Random graphs
Scaling limits
Descriptores:
Telecomunicaciones
Año de publicación:
2017
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Resumen:
We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds. Keywords : Random sequential adsorption, Scaling limits, Random graphs
Descripción:
Artículo publicado en Journal of Statistical Physics, v.169, 2017, pp. 989–1018
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Citación:
Bermolen, P, Jonckheere, M, Sanders, J. "Scaling limits and generic bounds for exploration processes". Journal of Statistical Physics, v.169, 2017, pp. 989–1018 https://doi.org/10.1007/s10955-017-1902-z
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Departamento académico:
Telecomunicaciones
Grupo de investigación:
Análisis de Redes, Tráfico y Estadísticas de Servicios
Licencia:
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
| Ficheros | Descripción | Tamaño | Formato | ||
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| BJS17.pdf | — | 681.65 KB | Adobe PDF |