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Probabilistic models for causal quantum gravity and scale dependent spectral dimension

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We study random walks on so-called multigraph ensembles, a specific class of random graphs relevant to theories of causal quantum gravity. In particular, we investigate the spectral dimension of the graph ensemble for recurrent as well as transient walks. Furthermore, the concept of scale dependent spectral dimension is introduced and models with different spectral dimension at different scales are analysed. We conclude by discussing a specific model relevant to quantum gravity which has a spectral dimension of four at large scales and two at small scales. The talk is based on work done in collaboration with G. Giasemidis and J. Wheater at Oxford.

No prior knowledge on quantum gravity is required.

This talk is part of the Probability series.

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