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Free keywords:
High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
Abstract:
The change of the effective dimension of spacetime with the probed scale is a
universal phenomenon shared by independent models of quantum gravity. Using
tools of probability theory and multifractal geometry, we show how dimensional
flow is controlled by a multiscale fractional diffusion equation, and
physically interpreted as a composite stochastic process. The simplest example
is a fractional telegraph process, describing quantum spacetimes with a
spectral dimension equal to 2 in the ultraviolet and monotonically rising to 4
towards the infrared.
