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# Non Unitary Random Walks

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Inria Paris-Rocquencourt, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : Motivated by the recent refutation of information loss paradox in black hole by Hawking, we investigate the new concept of {\it non unitary random walks}. In a non unitary random walk, we consider that the state 0, called the {\it black hole}, has a probability weight that decays exponentially in $e^{-\lambda t}$ for some $\lambda>0$. This decaying probabilities affect the probability weight of the other states, so that the the apparent transition probabilities are affected by a repulsion factor that depends on the factors $\lambda$ and black hole lifetime $t$. If $\lambda$ is large enough, then the resulting transition probabilities correspond to a neutral random walk. We generalize to {\it non unitary gravitational walks} where the transition probabilities are function of the distance to the black hole. We show the surprising result that the black hole remains attractive below a certain distance and becomes repulsive with an exactly reversed random walk beyond this distance. This effect has interesting analogy with so-called dark energy effect in astrophysics.
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Journal articles
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Cited literature [12 references]

https://hal.inria.fr/hal-00994977
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Submitted on : Thursday, May 22, 2014 - 2:25:23 PM
Last modification on : Sunday, June 26, 2022 - 12:01:22 PM
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### File

1349-5118-2-PB.pdf
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### Citation

Philippe Jacquet. Non Unitary Random Walks. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, Vol. 12 no. 2 (2), pp.333-362. ⟨10.46298/dmtcs.480⟩. ⟨hal-00994977⟩

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