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Abstract The recently proposed theory of “Asymptotically Free Mimetic Gravity” is extended to the general non‐homogeneous, spatially non‐flat case. We present a modified theory of gravity which is free of higher derivatives of the metric. In this theory asymptotic freedom of gravity implies the existence of a minimal black hole with vanishing Hawking temperature. Introducing a spatial curvature dependent potential, we moreover obtain non‐singular, bouncing modifications of spatially non‐flat Friedmann and Bianchi universes.
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Invariant measures for stochastic conservation laws on the line
Abstract We consider a stochastic conservation law on the line with solution-dependent diffusivity, a super-linear, sub-quadratic Hamiltonian, and smooth, spatially-homogeneous kick-type random forcing. We show that this Markov process admits a unique ergodic spatially-homogeneous invariant measure for each mean in a non-explicit unbounded set. This generalises previous work on the stochastic Burgers equation.
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- PAR ID:
- 10529424
- Publisher / Repository:
- Nonlinearity
- Date Published:
- Journal Name:
- Nonlinearity
- Volume:
- 36
- Issue:
- 9
- ISSN:
- 10.1088/1361-6544/acdb3a
- Page Range / eLocation ID:
- 4553 to 4584
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1361-6544/acdb3a
