# Non Unitary Random Walks

1 HIPERCOM - High performance communication
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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Reports

Cited literature [4 references]

https://hal.inria.fr/inria-00400816
Contributor : Philippe Jacquet <>
Submitted on : Wednesday, July 1, 2009 - 5:55:09 PM
Last modification on : Wednesday, September 16, 2020 - 5:04:10 PM
Long-term archiving on: : Monday, October 15, 2012 - 3:00:52 PM

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nonunitarywalk-RR.pdf
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• HAL Id : inria-00400816, version 1

### Citation

Philippe Jacquet. Non Unitary Random Walks. [Research Report] 2009. ⟨inria-00400816⟩

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