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arXiv · 1301.3486

Backbone scaling limit of the high-dimensional IIC

Markus Heydenreich·Remco van der Hofstad·Tim Hulshof·Grégory Miermont
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Abstract

We identify the scaling limit of the backbone of the high-dimensional incipient infinite cluster (IIC), both in the long- as well as in the finite-range setting. In the finite-range setting, this scaling limit is Brownian motion, in the long-range setting, it is a stable motion. The proof relies on a novel lace expansion for percolation that resembles the original expansion for self-avoiding walks by Brydges and Spencer in 1985. This expansion is interesting in its own right.

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Markus Heydenreich, Remco van der Hofstad, Tim Hulshof, Grégory Miermont. 2013-01-15. Backbone scaling limit of the high-dimensional IIC. https://arxiv.org/abs/1301.3486

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