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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2009

Non Unitary Random Walks

Philippe Jacquet

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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Dates and versions

hal-00994977 , version 1 (22-05-2014)

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