The impact of a random metric upon a diffusing particle

Abstract

We show that if the singularity of the quantized gravity propagator is $|\mathbf{x}{|}^{-2\gamma }$ then the mean value of the fourth power of the distance achieved in time $t$ by a diffusing particle behaves as $t^{2(1-\gamma )}$ for a small $t$.

arXiv comment12 pages, journal version

References in corpus (14)

• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe
• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• Gravitational Correction to Running of Gauge Couplings
• Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
• Dimension and Dimensional Reduction in Quantum Gravity
• Gauge Dependence of Gravitational Correction to Running of Gauge Couplings
• Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
• Heat Kernels and Zeta Functions on Fractals
• Spacetime foam: a review
• Quantum Geometry and Diffusion
• Universal regular short distance behavior from an interaction with a scale invariant gravity
• The spectral dimension in 2D CDT gravity coupled to scalar fields