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- Publisher
- Birkhäuser Basel
- Copyright
- © Birkhäuser Basel 2009
- ISBN
- 978-3-0346-0029-3
- Pages
- 197 –224
- DOI
- 10.1007/978-3-0346-0030-9_7
- Publisher site
- See Chapter on Publisher Site
Abstract
[We review some aspects of scaling limits of random planar maps, which can be considered as a model of a continuous random surface, and have driven much interest in the recent years. As a start, we will treat in a relatively detailed fashion the well-known convergence of uniform plane trees to the Brownian Continuum Random Tree. We will put a special emphasis on the fractal properties of the random metric spaces that are involved, by giving a detailed proof of the calculation of the Hausdorff dimension of the scaling limits.]
Published: Dec 30, 2009
Keywords: 60C05; 60F17; Random maps; random trees; scaling limits; Brownian CRT; random metric spaces; Hausdorff dimension